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A Maxent-based model for identifying local-scale tree species richness patch boundaries in the Lake Tahoe Basin of California and Nevada

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A Maxent-based model for identifying local-scale tree species richness patch boundaries in the Lake Tahoe Basin of California and Nevada

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A MAXENT-BASED MODEL FOR IDENTIFYING LOCAL-SCALE TREE SPECIES
RICHNESS PATCH BOUNDARIES IN THE LAKE TAHOE BASIN OF CALIFORNIA AND
NEVADA

by

James J. Pollock

A Thesis Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOGRAPHIC INFORMATION SCIENCE AND TECHNOLOGY)

August, 2015

Copyright 2015 James J. Pollock
ii
DEDICATION
I dedicate this work to my parents, Scott and Maureen. Your pride in me is my strength and
motivation. This document could not exist without you.

iii
ACKNOWLEDGMENTS
My warmest thanks to the remarkable people that guided and supported my journey to a Master’s
degree.
Writing a thesis is a sometimes lonely and always daunting task. My thesis advisor, Dr.
Travis Longcore expertly administered the perfect mix of sage advice, encouragement and
occasional kicks in the pants to keep me on point, on task and on pace. More importantly, he
pushed me to delve deeply into the ecology behind my topic—the final product is many times
better than I would have produced on my own.
The members of my thesis committee, Dr. Karen Kemp and Dr. Su Jin Lee provided
mentorship long before my thesis project began. Their enthusiasm for all things geospatial is
infectious and I could not ask for a finer pair of mentors. My thesis is quite a tome; their patient
critiques are most appreciated.
Finally, to my family, Tami, Madison, Morgan and Murphy. Your dinner deliveries,
patience and hugs contributed to my success more than you know.

iv
TABLE OF CONTENTS
DEDICATION ii
ACKNOWLEDGMENTS iii
LIST OF TABLES viii
LIST OF FIGURES ix
LIST OF EQUATIONS xi
LIST OF ABBREVIATIONS xii
ABSTRACT xiv
CHAPTER 1: INTRODUCTION 1
1.1 Research Questions 3
1.2 Motivation 5
1.3 Workflow 7
CHAPTER 2: BACKGROUND 9
2.1 Species Richness 9
2.2 Conceptual Model 12
2.3 Appropriateness of Maximum Entropy for Species Richness Modeling 16
2.4 Maximum Entropy Theory 19
2.5 Additional Relevant Maxent Studies 20
2.6 Species Richness Boundary Detection and Definition 22

v
CHAPTER 3: DATA AND METHODS 24
3.1 Data 24
3.1.1 Map Projections 24
3.1.2 Tahoe Basin Existing Vegetation Map (TBEVM) v.4.1 26
3.1.3 Tahoe Basin Digital Elevation Model (DEM) 32
3.1.4 Tahoe Basin SSURGO Soils Survey 34
3.1.5 Tahoe Area Weather Stations 37
3.1.6 TRPA Land Use and Completed USFS Prescriptions 40
3.2 Data Processing 42
3.2.1 Precipitation Surface Creation Using Empirical Bayesian Kriging 42
3.2.2 Data Consolidation 46
3.2.3 Tree Species Richness Attribute Calculation 47
3.2.4 Data Split by Management Intensity 48
3.3 Models and Analyses 48
3.3.1 Exploratory Ordinary Least Squares Regression 49
3.3.2 Species Richness-Based Maxent Model 51
3.3.3 Species Range-Based Maxent Model 56
3.3.4 Known Species Location Versus Predicted Species Range Map 57
3.3.5 Split Moving Window Dissimilarity Analysis (SMWDA) 58

vi
CHAPTER 4: RESULTS 61
4.1 Evaluation of EBK-Derived Precipitation Surface 61
4.2 Selection of Environmental Variables 65
4.3 Maxent Models 70
4.3.1 Common Procedural Issues 71
4.3.2 Species Range-Based Model 72
4.3.3 Species Richness-Based Model 77
4.3.4 Validation of Species Richness Models by Comparison 85
4.4 Split Moving Window Dissimilarities 87
CHAPTER 5: DISCUSSION AND CONCLUSIONS 93
5.1 Research Questions 93
5.1.1 Can the Maxent maximum entropy modeling package make valid
predictions of tree species richness patches? 93
5.1.2 Can the location and properties of border regions between Maxent
predicted species richness ranges be derived from Maxent output and if so,
are they valid? 95
5.1.3 Can the use of Maxent and a GIS produce a valid and broad scale
representation of tree species richness? 97
5.2 Discussion 97
5.2.1 Applicability of Species Richness Models to Forest Management 98
5.2.2 Relationship to Recent Research 100
5.2 Suggestions for Future Work 103
vii
5.2.1 Modeling Realistically Dense Data 103
5.2.2 Field Validation 103
5.2.3 Temporal Study 104
REFERENCES 105
APPENDIX 1: COMPLETE JACKNIFE ANALYSIS FOR SPECIES RICHNESS 113

viii
LIST OF TABLES
Table 1 TBEVM Species 29
Table 2 Species Richness Calculation 48
Table 3 Forest Management Categories 48
Table 4 Environmental Variables Selected from Exploratory Regression 66
Table 5 Statistical Diagnostics Following OLS 67

ix
LIST OF FIGURES
Figure 1 Study Area-Lake Tahoe Basin California/Nevada 2
Figure 2 Conceptual Model of Environmental Factors Leading to Species Richness Structure in
the Lake Tahoe Basin CA/NV 12
Figure 3 Common LTB Map Projections 25
Figure 4 Tahoe Basin Existing Vegetation Map v. 4.1 (TBEVM)—Tree Species Richness Data
Overview and Exploration 27
Figure 5 Species Richness Data Exploration Using Geostatistical Analysis 31
Figure 6 LTB 5m LIDAR-Derived Digital Elevation Model (Resampled to 30m Resolution) 33
Figure 7 SSURGO Soils Data—Mean Moisture Capacity (cu cm) 35
Figure 8 LTB Weather Stations and Preliminary Precipitation Surface 39
Figure 9 TRPA Land Use and Prescribed Treatments 41
Figure 10 Pre-Kriging Data Analysis (Stationarity, Autocorrelation, Normality) 44
Figure 11 EBK Precipitation Surface (Inches of Precipitation-Annual Mean) 45
Figure 12 Data Consolidation Tool (ArcGIS Model Builder) 47
Figure 13 Maxent Pre-Processing using AcGIS and Spreadsheet Applications 52
Figure 14 Maxent Iteration 54
Figure 15 Post Processing—Species Richness Method (ArcGIS) 56
Figure 16 Post-Processing--Species Range Technique (ArcGIS) 57
Figure 17 EBK Diagnostics (Model Fit and Residuals) 62
Figure 18 Precipitation Surface Prediction Standard Error 64
Figure 19 OLS Residuals—Histograms and Scatter Plots 68
x
Figure 20 Geographic Distribution of OLS Residuals (Over and Under Prediction—Fits Within 2
Standard Deviations) 69
Figure 21 Maxent SDMs for Tree Species Lake Tahoe Basin, CA/NV 73
Figure 22 LTB Maxent SDMs (binary) with Species Presence Overlay 74
Figure 23 Maxent Species Richness Regions—Species Range Method, LTB, CA/NV 76
Figure 24 Maxent Tree Species Richness Distribution Models, LTB, CA/NV 78
Figure 25 Maxent Area Under Curve (AUC) Analyses for LTB Tree Species Richness
Distribution Models 80
Figure 26 Jacknife Analysis for 3 Species 81
Figure 27 Tree Species Richness Distribution Model for Zero Species: Raw Maxent Output for
Lake Tahoe Basin CA/NV 82
Figure 28 Maxent Derived Tree Species Richness Border Regions—Species Richness Method:
Lake Tahoe Basin CA/NV 84
Figure 29 Model Comparison: Tree Species Richness Models—Species Range Method (top) vs.
Species Richness Method (bottom) 86
Figure 30 SMWDA Sampling Location North Lake Tahoe, CA/NV 88
Figure 31 Split Moving Window Dissimilarity Analysis (6 Pt. Window) 90

xi
LIST OF EQUATIONS
(1) Simpson Diversity Index 50
(2) Upper Window Average 60
(3) Lower Window Average 60
(4) Dissimilarity Index 60
(5) Mean Dissimilarity (For Monte Carlo) 60
(6) Standard Deviation of Dissimilarity (For Monte Carlo) 60
(7) Dissimilarity Z-Score 60

xii
LIST OF ABBREVIATIONS
ASCII American Standard Code for Information Interchange
AUC Area Under Curve
BEF Biodiversity Ecosystem Functioning
CSV Comma Separated Values
DEM Digital Elevation Model
EBK Empirical Bayesian Kriging
GIS Geographic Information System
LIDAR Laser Identification Detection and Ranging
LTB Lake Tahoe Basin
LTBMU Lake Tahoe Basin Management Unit
MEM Maximum Entropy Model
NDVI Normalized Difference Vegetation Index
OLS Ordinary Least Squares
ROC Receiver Operating Curve
ROR Relative Occurrence Rate
SDM Species Distribution Model
SMSS Shifting Mosaic-Steady State
SMWDA Split Moving Window Dissimilarity Analysis
SSURGO Soil Survey Geographic Database
TBEVM Tahoe Basin Existing Vegetation Map
TRPA Tahoe Regional Planning Agency
UC University of California
xiii
UNR University of Nevada, Reno
USDA United States Department of Agriculture
USFS United States Forest Service
UTM Universal Transverse Mercator

xiv
ABSTRACT
The Lake Tahoe Basin, California/Nevada is the setting for evaluating a species richness
modeling technique that is both accessible and provides an apparently unique approach to
studying forest diversity patterns. Species richness, the total number of species of a focal group
present in an ecological community without regard to individual taxa, is an important indicator
of biodiversity. Despite its importance to researchers and natural resource managers, predicting
species richness patterns in forested landscapes is difficult and therefore, not common. The
computationally powerful yet highly accessible Maxent package, specifically designed for
modeling species distributions, is used to predict homogenous patches of species richness by
treating species richness values as individual “species.” Areas where ranges of homogenous
species richness overlap are then isolated and displayed as “border regions” similar to ecotones.
Nowhere in the ecological literature is Maxent used in this manner, nor are transitional zones
between regions of species richness viewed as spatial entities. Therefore, this thesis investigates
if Maxent can make valid predictions about species richness and if areas where species richness
predictions overlap constitute transition zones. To validate the model, traditional species
distribution models for each included tree species were created using Maxent, stacked and then
summed to produce a comparable species richness surface. Similar patterns between the two
models indicate that Maxent accurately predicts species richness from environmental factors.
Border regions were validated as legitimate spatial entities using split moving window
dissimilarity analysis—a technique used to identify ecotones. Results indicate that using Maxent
for this application is very likely valid and species richness border regions represent a promising
spatial entity for studying diversity patterns. This spatially explicit approach provides an
xv
accessible method for studying species richness patterns at multiple scales. Further, a temporal
series of these models provides a method for examining how diversity changes over time.
1
CHAPTER 1: INTRODUCTION
Species richness is defined as the number of species of a focal group present in an ecological
community without regard to any specific taxa. As an indicator of diversity, it is a useful
indicator of the health, structure and productivity of forest ecosystems (Adams 2009). For
example, high species richness is associated with high productivity due to factors such as
interspecific interaction or niche partitioning (Morin et al. 2011, Zhang et al. 2012). Conversely,
extremely high species richness is not necessarily desirable. Morin et al. (2011) observed that
productivity increases with richness, but productivity levels out at a consistent species richness
value. The interaction of disturbance and richness-induced productivity vary the species
carrying capacity of individual patches (Adams 2009). These phenomena and many other
diversity factors are of great interest to scientists and forest managers.
This research provides an accessible geospatial method that predicts local-scale species
richness patches using a maximum entropy analysis (via the Maxent species distribution
modeling package) and then treats overlap between them as transition zones. By treating
homogenous richness patches (or collection of patches) as ecological communities, properties of
transition zones that separate them such as their position, shape and abruptness can be mapped
and observed. The primary assumption is that in the real-world landscape, individual pixels may
only harbor one species richness value. Pixels that simultaneously predict multiple species
richness values combine to form an ecotone-like structure separating areas of more stably
defined diversity. This provides more information than a simple mapping of predicted richness.
Border regions delineate islands of diversity and depending on representation, may indicate the
abruptness of the transition. The Lake Tahoe Basin (LTB) (Figure 1) provides an excellent
2
setting for presenting this approach due to its rich data availability and its status as a distressed
ecosystem.

Mid-nineteenth-century Anglo-American immigrants clear-cut ponderosa pines (Pinus
ponderosa) in the LTB to supply timber to the nearby Comstock Lode. Later, tourism induced
development and near complete fire suppression further altered its structure (Raumann and Cablk
Figure 1 Study Area-Lake Tahoe Basin California/Nevada
The study area is defined by the jurisdiction of the Tahoe Regional Planning
Agency (TRPA). The Basin straddles the States of California and Nevada and
is situated in the Sierra Nevada Mountains approximately 200 mi. east of San
Francisco, CA and 30 mi. south of Reno, NV.
3
2008). The LTB is now less resilient to natural disturbances so large tracts of trees are perishing
from insect attack and disease; further, slash accumulating in the forest understory threatens
devastating wildfire (Taylor 2014).
Currently, the US Forest Service is thinning and restructuring the Basin’s forests into a
pre-settlement structure as a first step toward a species configuration conducive to predicted
future conditions. Patterns of diversity are indicators of both the forest’s current state and the
results of restoration efforts (U.S. Department of Agriculture 2013).
The Tahoe Basin is not alone. As of 2014, an estimated 2 billion ha of forest in the
United States are degraded due to human activity. Four general approaches, revegetation,
ecological restoration, forest landscape restoration and functional restoration, exist to restore
degraded forests (Stanturf, 2014). In some manner, each of these methods affects species
richness by (intentionally) inducing a disturbance. Given the influence of diversity on ecosystem
health, any tool that clearly presents forest structure through the lens of species richness is an
invaluable asset to those charged with researching and making forest management decisions.

1.1 Research Questions
A series of research questions form the core of this research. The questions build upon each
other addressing: the viability of creating tree species richness predictions using Maxent, the
validity of its output and finally, if that output may (or should) be further processed in a GIS.
1. Can maximum entropy habitat modeling produce a valid and broad scale representation of
tree species richness?
A variety of ways are available to predict species richness. For example, at a regional scale a
remote sensing algorithm expands the normalized difference vegetation index (NDVI) to predict
4
tree species richness (Waring et al. 2006). On more local scales, techniques that leverage species
area models (SAM) or species accumulation curves are common (Ugland et al. 2003).
Unfortunately, these are often computationally difficult and they are rarely spatially explicit.
Ideally, tree species richness could be extrapolated from sampled data; however, this is
notoriously difficult (Lam and Kleinn 2008). As a black-box maximum entropy modeling
package, Maxent both handles the heavy mathematics and is capable of producing broad scale
predictions based on sampled (presence only) data.
Maxent is designed to predict the ranges of individual species based on sparse
observations and environmental data, not species richness. Therefore, the second research
question addresses the validity of using Maxent in this way.
2. Can the Maxent maximum entropy modeling package make valid predictions of tree species
richness patches?
This question of validity is somewhat subjective. The most important element of resolving this
issue is defining criteria that relate to the model’s purpose and context (Rykiel 2006). No perfect
algorithm, however complex, exists for predicting species richness. Therefore, it is unreasonable
to expect Maxent to predict the specific species richness value for any given surface pixel.
Rather, it is expected that, as a valid method Maxent will predict ranges of species richness that
generally agree with actual observations and provide a useful indication of structure and change
across the study area.
The study of borders and ecotones is an exciting and growing area of study in ecology,
which leads to the next research question.

5
3. Can the location and properties of border regions between Maxent predicted species
richness ranges be derived from Maxent output and if so, are they valid?
Maps of valid species richness border regions provide a cleaner and richer depiction of a forest’s
diversity structure. The question of validity is also relevant for this element of the model,
however. Exactly what defines a border region or ecotone is a matter of debate in the literature.
Given this model is based on predictions derived from probability, it is possible overlapping
regions are simply the result of variation in the predictions. Techniques exist in the literature to
identify legitimate ecotones, so if transitions between species richness ranges are meaningful,
they should be detectable using those methods.

1.2 Motivation
Academic literature focused on species richness and diversity widely agrees that managing
diversity is critical to effective forest conservation and restoration efforts. For instance, Xu et al.
(2012) exclaim species richness information is critical for assessing “biodiversity, conservation,
and extinction risk in the face of climate change and anthropogenic disturbance” (p. 1006).
Morin et al. (2011) conducted an extensive study correlating tree species richness to forest
productivity.
Many authors also concur that estimating species richness from sampled data is difficult.
(Graham and Hijman 2006, Lam and Kleinn 2008, Xu et al. 2012). A geospatial technique that
effectively predicts zones of consistent species richness and then identifies the location and
properties of border regions between them addresses both of these issues.
A search of the literature produced no practical application of maximum entropy to create
a species richness distribution surface. An investigation by Xu et al. (2012), however, addressed
6
the problem of species richness’s sensitivity to scale (Crishom et al. 2013). The authors assessed
whether twelve quantitative methods could upscale locally sampled species richness to a regional
level. The authors opined that for heterogeneous landscapes, the maximum entropy method
performed the best. The excellent performance of maximum entropy in a species richness
application is encouraging given the popularity and relatively easy access to the maximum
entropy algorithm provided by the Maxent modeling package (Phillips et al. 2006). The specific
mathematics evaluated by Xu et al. differ somewhat from Phillips et al., but they are anchored by
the same theory. Given this, an evaluation of Maxent output for this application is worthwhile.
The Lake Tahoe Basin provides an excellent opportunity to utilize and evaluate the
maximum entropy method in a practical species richness investigation. An investigation of
Northern boreal forests would primarily feature regional (gamma) scales whereas a small
conservation area would likely examine local (alpha) scale diversity. In contrast, the spatial
extent of the Lake Tahoe Basin is such that diversity patterns are relevant at fine granularity as
well as at wider scales (alpha-beta) (Whittaker 1960). These factors add particular interest to
investigating the performance and utility of a maximum entropy method given the findings of Xu
et al. (2012).
While plotting raw Maxent predictions of species richness provides useful information
regarding the dispersion of tree species diversity, the structure of Maxent output rasters allow for
post-processing to display border regions. There are two benefits to extending the analysis this
way. First is clarity of the representation. Maxent does not produce predictions of neat polygons
with coincident borders. Rather, numerous pixels are identified as suitable for multiple species
richness values. Displaying these areas as borders between areas of homogenous zones of
species richness reduces clutter in the representation and better highlights patterns. Second, the
7
width, shape and abruptness of border regions provide important clues as to the underlying
mechanisms that shape diversity patterns. Lastly, species richness border zones provide new,
tangible spatial objects for scientists and managers to investigate (Kroger 2009).

1.3 Workflow
The workflow for this research followed a stepwise path from planning to interpretation.
Specifically, the research plan was to determine appropriate environmental factors, construct the
models and then validate them.
1. Establish data needs (Maxent environmental variables)
The scientific literature and simple brainstorming identified a list of biotic, abiotic and
anthropogenic factors that influence species diversity in the LTB.
2. Gather required datasets
Several spatial datasets provided input variables to the models constructed for this research:
 Tahoe Basin Existing Vegetation Map (TBEVM)
 Tahoe Basin Digital Elevation Model
 Tahoe Basin Soils Survey (SSURGO)
 Tahoe Area Weather Stations
 TRPA Land Use
3. Process datasets
Raw datasets were processed to consolidate datasets and derive attributes not explicitly provided
by the dataset authors.

8
4. Exploratory regression
The ArcGIS Ordinary Least Squares (OLS) exploratory regression tool iteratively created
regression models to select the most appropriate independent variables for use in the Maxent
models.
5. Species richness-based maximum entropy model (MEM)
This model highlights ranges of tree species richness communities (e.g. 2 species, 3 species, etc.)
and then intersects them to identify the position, width, shape and abruptness of overlapping
predictions.
6. Species based Maximum entropy model
This validation model adds Maxent-derived species distribution models (SDM) for each relevant
tree species—a stacked species distribution model. If both models in this study are valid, the
resulting surfaces should be similar (e.g. Dubuis (2011).
7. Known species vs. predicted range map
While Maxent is specifically designed to predict species ranges, this output must also be
validated. If the Maxent predictions encompass point data of known species, the Maxent
predictions may be considered reasonable.
8. Split moving window dissimilarity analysis (SMWDA)
SMWDA is a common method used in ecotone studies (e.g. Hennenberg 2005, Kroger 2009).
This analysis validates that overlapped Maxent predictions of species richness represent
transitions between areas of diversity.
Chapter 2 provides an overview of peer-reviewed literature that support the premises and
methods used in this research.

9
CHAPTER 2: BACKGROUND
This chapter reviews literature related to this research. In some instances, evidence from
reviewed literature is synthesized to provide the basis for assumptions made in this project (e.g.,
species richness conceptual model). The topics proceed from prevailing theory behind species
richness and maximum entropy modeling to practical issues such as parameter setting in the
Maxent package.

2.1 Species Richness
The thrust of this research is to provide scientists and managers a tool to view the distribution of
tree species richness across a study area. The utility of such information derives from the nexus
between species diversity and ecosystem function. A significant body of literature explores this
connection, termed biodiversity ecosystem functioning (BEF; Morin, 2011), from a variety of
angles ranging from climate change to management technique. In the context of this research,
several of these studies are leveraged to develop a conceptual model of species richness pattern
development.
An excellent starting point for exploring species richness is the deep analysis provided by
Jonathan Adams in his book, Species Richness (2009). Adams defines species richness as the
total number of species present without regard to density. His first chapter explores local scale
species richness which in his words are “applicable to scales ranging from a few centimeters to
several tens of kilometers” (p. 7). This differs from the classic alpha, beta, gamma diversity
scales proposed by Whittaker (1960), but as Adams laments, the complexity of ecological
systems precludes a unified theory. For the purposes of this investigation, Adam’s local scale
seems most appropriate.
10
In sessile communities (e.g. trees), Adams lists three primary factors that affect the local
species richness:
 Recovery from a single large disturbance
 Varying frequency and intensity of disturbances across an area
 Varying quality of substrate such as soils, slope, elevation, aspect
These criteria cover significant ground. Discrete disturbances might include a clear
cutting event or perhaps a natural fire. Frequency of sustained disturbance can relate to climate
patterns or perhaps the level and type of routine management activity. The last item
encompasses any substrate variable such as slope, aspect or elevation.
Morin et al. (2011) provide a more pointed investigation that examines the relationship
between diversity and productivity using a forest succession model. The authors document
evidence that tree species richness promotes productivity in temperate forests via
complementarity between species. Specifically, a forest community that combines many species
with varying shade tolerances and abilities to grow in degraded environments enhances a forest’s
ability to recover from small-scale disturbance. The authors note that productivity is related to
species richness levels. Adams (2009) discusses this concept as it relates to local-scale richness.
He proposes that a balance between disturbance and productivity affects species-specific
carrying capacity. A particularly relevant item gleaned from Morin et al. (2011) is their use of
soil moisture capacity in their models. That variable is used as an environmental factor
representing soil quality in this study.
DeClerck et al. (2006) provide insight into the specific effects of species richness on the
Lake Tahoe Basin. The researchers studied species richness in the Desolation Wilderness area of
the LTB with a focus on stand stability derived from species richness. Of particular interest are
11
their environmental variable selections of elevation, slope and aspect and community response
variables of species percentage, basal area and canopy closure. The results of this study are
interesting. The authors found that increasing species richness in the Desolation Wilderness
correlates with increased resilience (the ability to recover from disturbance) but not resistance
(tolerance of disturbance).
Martin-Quellar et al. produced two relevant studies (2011 and 2013) that address
management effects on species richness. The caveat to the applicability of these studies is that
they investigate gamma scale diversity in Central Spain. This limits their specific applicability
to this study somewhat, but they are the only studies of this nature addressing this critical
element. The 2011 study utilized geographically weighted regression to examine the effects of
management on species richness. The particularly salient conclusion is that biodiversity models
are more effective where management practices are incorporated and that management effects on
species richness were stationary across their study area. Further relevant conclusions include
observations that tree species richness closely correlates with basal area and annual precipitation.
Martin-Quellar et al. (2013) used Bayesian statistics to further investigate the
biodiversity-management style connection focusing on the effects of silviculture. This is
particularly applicable to the Tahoe Basin because active restoration efforts have been ongoing
for some time. General observations by the authors indicate that moderate intensity disturbances
(natural or induced) contribute to species richness. Also of interest to this study is the authors’
conclusion that a hierarchy of variables, chiefly climate, affects the overall influence of
management and other disturbance types on species richness.

12
2.2 Conceptual Model
Ideas and conclusions from the literature in section 2.1 were synthesized into a conceptual model
for species richness structure graphically depicted in Figure 2. Specifically the graphic depicts a
systems-based hypothesis regarding how the environmental elements used in the Maxent model
combine to shape a forest structure made up of varying species richness patches.

The conceptual model is rooted in Stephen Hubbell’s Unified Neutral Theory of
Biodiversity and Biogeography (Hubbell 2008). The theory treats trophically similar species (in
this case, montane conifer and deciduous riparian trees) as ecologically identical (i.e. equally fit
to their environment). Competition between species is discounted in favor of random births,
deaths, speciation and dispersal as the mechanisms for creating biodiversity. This is a useful
Figure 2 Conceptual Model of Environmental Factors Leading to Species Richness
Structure in the Lake Tahoe Basin CA/NV
The conceptual model graphically depicts the biotic, abiotic and anthropogenic environmental factors
captured by the species richness prediction models. Factors are arranged into a theoretical system based
on evidence in related literature and Hubbell’s Unified Neutral Theory of Diversity and Biogeography
(Hubbell 2008). The goal is to produce a systems-based model whose output is tree species richness
structure in the Lake Tahoe Basin.
13
assumption given the number of species present is the only important output of this model. The
specific species contributing to the species richness values may vary and remain anonymous.
The inclusion of niche-determining factors (far left panel) is counterintuitive given
Neutral Theory discounts niches as a contributing factor to biodiversity. Following the
publication of Hubbell’s theory in 2001, several papers suggested that Neutral Theory is
inadequate in isolation, requires unrealistic auxiliary assumptions and spatially explicit versions
are limited in their descriptive power (Etienne and Rosindell 2011). Gewen (2006) suggests that
neutrality should be considered a backdrop or null hypothesis. Another paper opines that Neutral
Theory by itself is too extreme. Stabilizing influences (e.g. niche-forming factors) play roles in
biodiversity to degrees that vary by specific community (Adler 2007).
This model accepts that known biotic and abiotic factors, identified in the literature and
prioritized using regression, influence tree species richness in the LTB; however, the niches are
not defined classically. Hubbell’s Neutral Theory is an extension of island biogeography. As
such, niches formed by the factors in the far left panel most accurately represent distinct
communities that support a finite number of tree species drawn from the pool of species present
in the LTB. Clearly, these “island” communities are contiguous; therefore, allopatric speciation
is unlikely to be a significant driver of biodiversity in the LTB. Random birth, death and
especially seed dispersal (e.g., Barringer et al. 2012), however, are very plausible mechanisms.
Mixing ecological drift (neutral factors) and competitive factors into a single model is not
unprecedented. For example, Orrock and Watling (2010) created a biodiversity model that tests
their theory that community size is the mediating nexus between neutral and competitive factors.
The middle panel of the conceptual model incorporates shifting mosaic-steady state
(SMSS) as proposed by Borrmann and Likens (1994) to represent natural disturbance and
14
resulting secondary succession in the ecosystem. Adams (2009) stresses the heavy role of acute
and chronic disturbances in defining the species richness of local-scale plant communities. In
fact, Adams illustrates that an intermediate level of disturbance (versus no disturbance or
catastrophic disturbance) generally results in optimum species richness. SMSS is somewhat
controversial (as is Neutral Theory) because it represents a climax condition. Perry (2002)
presents an exhaustive discussion of this debate and the shift in thinking brought about by the
emergence of spatial ecology. The intent here is not to make a claim as to the existence of
SMSS; rather, its inclusion in the model provides a convenient way to represent disturbance and
succession. SMSS is not entirely theoretical, however. A recent study documented evidence of
SMSS approximately 100 miles north of Lake Tahoe in the Lassen Volcanic National Park,
California (Wang and Finley 2011). These factors are commonly accepted across the ecological
literature even if their specific ramifications are debated (Perry 2002).
SMSS represents niches (species richness “islands”) that are inherently stable. Neutral
Theory presumes succession by random colonization of disturbed landscape patches versus a
static climax state. This model presumes, however, climax states (or at least intermediate seres)
exist for periods of time even if they are short. During those periods, community sub-patches are
subject to localized disturbances such as natural fire, avalanches, etc. Disturbed patches move
through successional stages (e.g. meadow/brush sparse/sun-adapted forest dense mature
forest). The conclusions of DeClerck et al. (2006) regarding resistance and resilience tend to
support this hypothesis in the LTB. The random nature of these disturbances ensures a shifting
micro-landscape, but overall niche stability.
An SMSS disturbance model meshes well with Neutral Theory if we accept an
individualistic view of succession (Gleason 1926). The individualistic view assumes that
15
patches left barren by disturbance will be randomly colonized by a species well-adapted to local
conditions. The specific species that colonizes a barren patch is irrelevant; the aggregated result
of multiple random disturbances and succession within a community will be a steady mean value
of species richness. This process in isolation would logically result in a perpetual climax state
(e.g. SMSS). Both the individualistic view of succession and Neutral Theory accept that
environmental variables that define niches degrade over time resulting in ecological drift (and
perhaps a change in maximum species richness). For instance, climate change may alter mean
annual precipitation or, significantly in the LTB, management practices may mechanically
remove certain species.
The final (far right panel) incorporates non-natural influences into the model. Regression
analysis revealed that basal area is a major contributor to species richness in the LTB. Basal area
is defined as the total forest floor coverage of living tree stems (expressed as area/area). A
review of relevant literature reveals that its impact on species richness is well documented.
Basal area is a common indicator of primary productivity, which is a proxy for forest health and
structure as affected by biodiversity (Sagar and Singh 2006. Adams 2009, Chrisholm 2013).
Basal area also reflects time since disturbance, land use history, stand heterogeneity, and ongoing
succession; that is, it is an indicator of modification by the local environment (Lohbeck et al.
2012).
In sum, basal area is a community response variable. Its function in the model is to
capture unusual (non-parameterized) events such as disease or insect attack that act to reduce
basal area via mortality and, importantly, the presence or absence of human management activity
such as prescribed thinning, burning or cutting for convenience (e.g. to facilitate development).
Clearly, every removed tree reduces total basal area and constitutes a disturbance.
16
Finally, red boxes along the bottom of the model separate human management into
discrete events and continuous disturbance. A single anthropogenic disturbance (a prescribed
burn for instance) is likely absorbed into the ecosystem similarly to a natural event such as a
wildfire or avalanche. Ongoing policy, such as maintaining a ski resort or an urban landscape
fundamentally alters the underlying niche discriminators that produce species richness patches.
Species richness patterns are often predicted by stacking species distribution models
tailored to each species present in the ecosystem (SDM, Dubuis et al. 2011, Cord et al. 2014).
An individual species SDM is the output of an ecological system. This model illustrates that
species richness distributions are also the output of an ecological system. In other words, a
spatially explicit species richness model may be extracted from relevant biodiversity factors
(Dubuis 2011). A major goal of this research is to show that both approaches (utilizing
maximum entropy) will arrive at functionally equivalent solutions.

2.3 Appropriateness of Maximum Entropy for Species Richness Modeling
The maximum entropy algorithm for constructing area-based models is used in this study. The
typical use of this algorithm is for range estimation for single species from presence-only data
(Phillips et al. 2006). No practical use of this method for species richness modeling was found in
the literature; however, several journal articles lend credibility to the method.
Graham and Hijmans (2006) compared the efficacy of three techniques for mapping
species ranges and species richness. Specifically, the authors evaluated maps drawn by experts,
maps produced by species distribution modeling, and hybrids of the two methods. The authors
explicitly describe their use of Maxent for species range maps including variables, settings, and
evaluation. As for species richness mapping, the authors state they evaluated a map created by a
17
“distribution model” (p. 583); however, they are unclear as to the specific procedure they used to
create it. Given their use of Maxent for their species range map, it is likely they used Maxent for
this application as well, although it is unlikely they treated species richness values as individual
species. The relevant conclusions of their study are that distribution model-derived richness
maps tended to overestimate species richness versus hybrid maps but performed well.
Xu et al. (2012) evaluated twelve procedures for estimating species richness at a regional
scale from local scale samples. Six of these are non-parametric incidence-based methods, and
six are area-based methods, including maximum entropy. The authors use the term, MaxEnt;
however, they are referring to the maximum entropy method rather than the Maxent application
itself. Further, Xu et al. are not attempting to derive species richness from environmental
factors, they extrapolate species richness from area. The mathematics and end goal of Xu et al.
are different from the present study; however, the underlying maximum entropy approach,
estimating an unknown distribution based on sampled data, is similar. Importantly, the authors
successfully applied maximum entropy to a species richness problem and concluded that the
maximum entropy procedure was the best performing algorithm in their test set. Additionally,
they made the same overall assessment as Graham and Hijmans (2006). That is, the algorithm
overestimates species richness versus known plots by as much as 40%. Xu et al. does not
provide conclusive evidence that maximum entropy is appropriate for this application, but their
similar results to Graham and Hijmans and success in a species richness application add
credibility to the procedure proposed by this research.
Another important study is Dubuis et al. (2011). The researchers directly compared
species richness predictions derived from a macroenvironmental model (inferring species
richness from relevant environmental predictors) and stacked SDMs. The authors did not create
18
spatially explicit models; rather, they used statistical techniques. The study concluded that the
two methods were functionally identical; however, each had unique strengths and weaknesses.
Interestingly, the authors suggest that combining the two techniques could provide the most
accurate predictions. Aside from being non-spatially explicit, Dubuis et al.’s study is remarkably
similar to this research. Their methods lend credibility to the procedures used in this thesis and
their conclusions support validation by comparing stacked SDM and species richness-based
models.
A less specifically relevant, but interesting, study is Kolström and Lumatjärvi (1999).
The authors developed a decision support model designed to predict the effect of forest
management decisions on species richness. The model is more complex than the maximum
entropy-based model proposed by this research. Specifically it is a simulation that incorporates
high granularity variables such as decaying wood, stem diameter, and distribution by species.
The most relevant component of this extensive modeling effort is an opinion offered in its
conclusion, “Our system does not give absolute values for number of species in a stand, but the
results could be interpreted as a relative change in the number of species due to the change of
habitats. . .” (p. 55). This reflects the specific intent of this research and implies that a less than
optimal algorithm can deliver useful information.
None of this literature provides absolute assurance that Maxent is appropriate for this
application. Taken together, however, they imply that validation efforts are worthwhile and
likely to succeed.

19
2.4 Maximum Entropy Theory
Although Maxent is a black box-style modeling environment, a rudimentary understanding of its
underpinnings are essential to optimizing its use. Three sources were utilized to gain this
familiarity.
Elith et al. (2011) translates the machine-learning based mathematics of the Maxent
algorithm into statistical language more familiar to ecologists. The paper explores many aspects
of the Maxent environment, but the central topic is an explanation of maximum entropy theory
itself. Specifically, it relates that the model minimizes the relative entropy (a measure of the
distance between distributions) between two probability densities (one from the presence data
and one from the landscape).
Merow et al. (2013) is an overview of the settings in Maxent and how they ought to be
applied. The authors begin with an overview of the underlying mechanics of the Maxent
algorithm from a statistical perspective similar to Elith et al. (2011). This information is used to
support recommendations regarding model settings. The authors encourage Maxent-setting
decisions based on biological and study related factors rather than convenience or a lack of
understanding.
These articles are quite technical despite their intent to simplify maximum entropy.
Maxent’s web-based documentation is very accessible and was used to temper the difficult
reading of the formal articles. The following brief summary is a simple language overview of
Maxent based on these sources.
Maximum entropy is described by the statistical distribution that best fits the geographic
spread of samples and the background. Maxent calculates the maximum entropy input data
presence data as they relate to the “background.” The background is the sum of environmental
20
variables the user provides as explanatory variables. For those accustomed to the ArcGIS
environment, these raster datasets are counterintuitively known as “features.”
The process is similar to an exploratory regression; however, the maximum entropy
method is nonparametric, meaning it makes few data assumptions and is capable of creating
highly complex curves from samples drawn from multiple distributions. The benefit of this is
that Maxent can accept mixtures of feature data types such as continuous, categorical, interval
that would be difficult to process with ordinary regression techniques. Maxent internally
converts categorical data into interval data.
The resulting (raw) output is a relative occurrence rate (ROR) for each raster cell. This is
simply the likelihood that a cell is occupied by the same species as the sample set. This is not an
explicit probability that a cell is suitable habitat. That would require knowledge of the
population size. Rather, it is simply the likelihood that a cell is suitable habitat relative to the set
of other cells.

2.5 Additional Relevant Maxent Studies
Prates-Clark et al. (2008) used Maxent with remotely sensed presence data and climate
environmental data to investigate actual versus potential ranges of three tree species in the
Amazon Basin. Specifically, the researchers were interested in the efficacy of using remotely
sensed data in maximum entropy-type models. They compared statistical and predictive output
for climate data alone, remotely-sensed alone, and combined models. They found that remotely
sensed data is consistently superior as a stand-alone input (likely due to reduced sampling bias),
but it is limited because it cannot capture all processes that contribute to forest species
distribution. The study is highly relevant to the present study given Maxent is typically used to
21
analyze field-collected data. The TBEVM data used in this research is derived from IKONOS
satellite imagery and shares similar limitations as the remotely sensed data in this article.
TBEVM data is limited to detecting species observable in the canopy. Satellite imagery cannot
detect vegetation within the forest understory.
Smith et al. (2012) investigated the spatial extent and recruitment factors of acacia trees
in Southern Africa. While the subject matter of this investigation is not particularly relevant, its
scale is. The study area of Kruger National Park in South Africa is about 2.5 million ha—
roughly equivalent to the Lake Tahoe Basin. Most examples of Maxent use in the literature
involve much broader spatial extents than this study or the Lake Tahoe area (e.g. State or
continental-level). This study provides validation that Maxent output can be effective at a more
community-level scale.
York et al. (2011) modeled habitat for invasive tamarisk (a woody plant) and the
Southwestern willow flycatcher. Tamarisk replaces nesting habitat for the flycatcher. Biologic
control efforts introduced a beetle that is reducing tamarisk. The researchers used overlap of
Maxent predictions of highly suitable tamarisk and flycatcher habitat to predict most-suitable
areas for the biologic controls. This study is specifically post-processed Maxent output (e.g.
overlay) to achieve a research goal. Further, this study implies that the overlap of Maxent ranges
is meaningful, rather than artifacts of the prediction algorithm.
Maxent ranges are based in probability, so they inevitably contain some error. The
potential for error is further compounded by the noisy nature of ecological data. Stacking
predictions could compound their error to the point that the resulting surface contains more error
than meaningful data. As such, this study rigorously evaluated stacked surfaces to ensure they
are meaningful.
22
2.6 Species Richness Boundary Detection and Definition
An important objective of this research is to establish that overlapping Maxent species richness
ranges mark legitimate, meaningful boundary regions and not simple variation in the prediction
algorithm. Ecological boundaries and ecotones are a high interest topic in the ecological
literature (Cornelius and Reynolds 1991, Hennenberg et al. 2005, Kark and van Rensberg 2006,
Kroger et al. 2009). Although agreement is widespread that these zones are interesting and
significant, there is little consensus on how to define them. Kark and van Rensberg (2006)
surveyed recent trends on the subject and working from a variety of definitions in the literature,
they crafted a working definition of ecotone: An ecotone is an “area of steep transition between
communities, ecosystems, or biotic regions” often emphasizing the abruptness of the change (p.
32). Whether or not boundaries between areas of similar diversity are properly termed ecotones,
boundaries or some other phrase, is less important than if it is useful to identify them. By the
Kark and van Rensberg definition, ecotones are properly defined if they delineate homogenous
regions forged by natural processes. Species richness and biodiversity easily meet that criterion.
Whether Maxent output can effectively identify border regions is another matter. Kroger
et al. (2009) investigated boundary detection for riparian zones in the Kruger National Park,
South Africa. They emphasize that border detection is a matter of identifying changes in
underlying processes. Maxent predicts probability of occurrence based on variability in the
environmental data that represent these underlying processes. In discussing methods of
identifying ecological borders, Cornelius and Reynolds (1991) point to theory that these borders
act similarly to semi-permeable membranes where elements of adjacent homogenous units
percolate between each other or into an intermediate zone. It is not a great leap to suggest
overlapping homogenous Maxent predictions could represent this process.
23
Cornelius and Reynolds (1991) further suggest that ecotones and borders can be
identified by seeking discontinuities in transect data with a family of analyses called “split
moving window.” Kroger et al. (2009) and Hennenberg (2005) utilized split moving window
dissimilarity analysis (SMWDA) in their research involving border and ecotone identification.
SMWDA is relatively simple statistical procedure, but it is limited to identifying discontinuities
along two-dimensional transects. The Maxent method is less quantitatively rigorous, but it
allows for creating mappable representation of border regions across a large area. In the context
of this research, the established SMWDA method is used to validate the Maxent method. If
Maxent range overlaps represent border regions, then SMWDA discontinuities should coincide
with them.
This chapter summarized the role of species richness in ecosystems, provided theoretical
framework for predicting species richness from environmental variables. Additionally, the use
of Maxent to create species richness predictions was explored using examples from relevant
literature. Chapter 3 is an exhaustive description of the data and techniques used to undertake
this research.

24
CHAPTER 3: DATA AND METHODS
This chapter provides a detailed description of the datasets and methods used in this research.
The first section provides an evaluation of the properties and appropriateness for use of each
dataset followed by a description of how they were processed for use. The second section is an
accounting of the rationale for, and construction of, each model and procedure used in this
project.

3.1 Data
No spatial analysis is credible without a full evaluation of its input datasets. Further,
appropriately projecting data for any spatial analysis is a critical step. The geographic position
of the Lake Tahoe Basin makes choosing the best projection uniquely challenging, so this section
begins with a brief discussion of that issue. The remainder of the section is a thorough
evaluation of each dataset. The Tahoe Basin Existing Vegetation Map (TBEVM) is the primary
source of species richness data, so a more through exploration of that dataset is included.

3.1.1 Map Projections
All datasets in this project are projected to NAD 83 UTM zone 10. Selecting an appropriate
map projection for analysis in the Lake Tahoe area can be difficult. The Basin straddles the
boundaries for multiple UTM and State Plane projection systems (Figure 2). These are the
projection systems that best preserve area and distance at scales that usefully represent
geographic regions of this size (e.g. ~1:300,000). Lake Tahoe’s geography places it at a
disadvantage in this regard because no system perfectly suits Basin-wide studies. The Tahoe
Basin is distant from the central meridian of any usable standard projection and sits at high
25

elevation, so some distortion is unavoidable. Custom projections are an option for fine accuracy
work, but they make sharing datasets difficult. State Plane systems are not valid outside State
boundaries, so researchers must select a UTM zone or a broader projection scheme such as
Albers. While UTM zones 10 and 11 nearly bisect the Basin, zone 10 covers a slightly larger
Figure 3 Common LTB Map Projections
The most common map projections for the Lake Tahoe Basin are provide to illustrate a unique problem
facing spatial analysts in the LTB. The Basin straddles the boundaries of four map projection schemes,
none of which encompass the entire Basin. For Basin-wide studies, State-Plane systems are unusable,
leaving the extreme edge portions of UTM zones 10-11 as the most usable projections. Zone 10 is covers
the most area of the Basin and is the de-facto standard for LTB studies. In every case, some distortion is
inevitable and must be considered when evaluating the results of spatial analyses in this region.
26
area. NAD 83 zone 10 is not ideal, but it has become the (mostly) de facto standard for GIS
work by governing agencies in the Lake Tahoe area.

3.1.2 Tahoe Basin Existing Vegetation Map (TBEVM) v.4.1
TBEVM is the product of a UC Davis Center for Spatial Technology and Remote Sensing
project that used IKONOS satellite imagery to map vegetation in the Lake Tahoe Basin
(Figure 4). The dataset provides high granularity vegetation information that exceeds the detail
of any other publically available dataset.
 Representation: The dataset is a vector polygon model, so the data are technically discrete;
however, the extremely fine resolution of the polygons make it comparable to many raster
datasets (e.g. Landsat). The effect is to create a nearly continuous model when viewed at
moderate scales.
 Size: The dataset contains 20,693 discrete polygon objects.
 Scale: The extent of the dataset covers the Lake Tahoe Basin that totals 1330 sq. km.
Polygons in the dataset vary from 16m
2
to 100,000 m
2
. The underlying raster data have a 1-
m resolution.
 Aggregation: Polygons were aggregated from raster data on the basis of physiognomic
vegetation classes. The polygons represent best-fit vector overlays of vegetation classes
defined by agencies such as the US Forest Service (USFS) and the Federal Geographic Data
Committee. The resulting data reflect distinct micro-regions of homogeneous vegetative
communities.
27

Figure 4 Tahoe Basin Existing Vegetation Map v. 4.1 (TBEVM) —Tree
Species Richness Data Overview and Exploration
The Tahoe Basin Existing Vegetation Map is a product of the UC Davis Center for Spatial
Technology and Remote Sensing that utilized 2007 IKONOS satellite imagery to classify
existing vegetation in the LTB. Tree species richness data for this study was derived from
this dataset. The main figure displays the resulting species richness surface and the inset
illustrates the fine granularity of these data.
28
 Attributes: The dataset contains over fifty attributes derived from IKONOS classification and
analysis. Data of particular interest are percent coverage figures for nine individual tree
species.
Note that species richness is represented in Figure 4 to facilitate an initial overview of
the presence-only data used in this research. Species richness is not a native attribute in
TBEVM. The method used to create this attribute is described in section 3.2.3.
Over 40 additional attributes are included in the dataset. Some variables such as “basal
area” were directly assessed and utilized as Maxent feature data. Others, such as “stems per
hectare” provided the basis for derivative attributes.
 Fuzzy/Crisp: These data are matched to subjective ecological categories that crisply partition
a continuously varying forest landscape. The polygons effectively model forest structure in
aggregate; however, their individual boundaries are inherently fuzzy.
 Error: Error in these data is high as in any forest dataset. Remotely sensed data is error
prone due to misclassification and atmospheric anomalies. Beyond inherent remote sensing
error, this is an aging dataset. These data were obsolete the moment they were collected and
that error multiplies with age. The authors’ metadata includes accuracy estimates that vary
by attribute from 10 to 80%. The large size of the dataset works to balance error to a reliable
50% range. Age degrades that accuracy. The data do not represent the forest today, but it is
an excellent representative snapshot.
 Fitness for use: TBEVM contains a large percentage of the data used in this research, so it
was given a particularly close evaluation. The age of the data—circa 2007—is concerning
given field validation of derived datasets is desired, but TBEVM is the only publically
available dataset that can deliver species-level resolution. To maximize the probability of
29
success of this research, an extremely fine grained dataset was specifically sought. TBEVM
meets this criterion (Figure 3 inset). Ecological experts at UC Davis assembled these data, so
the data can be trusted as an accurate snapshot of Tahoe Basin forest structure as of the date
it was assembled.
While the data may be considered accurate as of their collection, they have inherent
limitations. First, they are limited to the resolving power of the author’s classification
algorithm. There are nine tree species classified (Table 1).

Species Code Scientific Name Common Name
ABCO Abies concolor white fir
ABMA Abies magnifica red fir
JUOC Juniperus occidentalis western juniper
PIAL Pinus albucaulis whitebark pine
PICO Pinus Contorta lodgepole pine
PIJE Pinus jeffreyi Jeffrey pine
PIMO Pinus monticola western white pine
POTR Populus tremuloides quaking aspen
TSME Tsuga mertensiana mountain hemlock

Two prominent species, Ponderosa pine and Douglas fir (Pseuudotsuga menziesii) are
excluded from the dataset as these species are indistinguishable from Jeffrey pine (Pinus
jeffreyi) using the author’s remote sensing technique. Second, remote sensors cannot “see”
into the understory level of a forest. The data are limited to a canopy view of the forest,
which may disguise pertinent elements of species richness such as early succession
recruitment of shade tolerant species. With these limitations understood, the dataset is well
suited for use in this project.
Geostatistical analysis was utilized to conduct an exploration of the TBEVM tree species
richness data (Figure 5). The top panel is a histogram of species richness. The data appear to be
Table 1 TBEVM Species
30
normally distributed except for a spike the lowest bin. This is probably attributable to urban
areas disturbing the natural distribution system.
The second panel is a typical snippet of an entropy Voronoi analysis for the dataset. The
data appear to be non-stationary.
The last panel is a trend analysis that graphically depicts an increasing richness values
moving away from the lake (and increasing in elevation).
Notably absent is a semivariogram. The downside of a high granularity dataset covering
a large area is that it may exceed software capabilities or computer memory limitations. Memory
limitations precluded the construction of a semivariogram for these data.

31

Figure 5 Species Richness Data Exploration Using Geostatistical Analysis
The ArcGIS geostatistical toolbar provides further exploration of the species richness data
derived from the TBEVM dataset and displayed in Figure 4. The top panel is a histogram of
the species richness data. The data approximate a normal distribution except for a spike in
the lowest bin, possibly attributable to anthropogenic disturbance in urban areas. The middle
panel is an entropy Voronoi diagram section used for assessing the stationarity of the data.
The data appear non-stationary. The bottom panel is a trend diagram that suggests an
increasing species richness trend moving away from the center of the dataset (Lake Tahoe) in
the x (E-W) and y (N-S) directions.
32
3.1.3 Tahoe Basin Digital Elevation Model (DEM)
DEMs are a raster model of elevation data. This LIDAR-derived Digital Elevation Model
(Figure 6) was assembled by the San Diego Supercomputing Center utilizing public domain
point cloud data provided by TRPA.
 Representation: The native dataset is a 5x5 meter raster model whose data indicate the mean
elevations of first returns (e.g. treetops) and ground returns (for bare ground) from a LIDAR
sensor. LIDAR point densities for first returns average 11.82 points per square meter, while
ground returns average 2.26 points per square meter. To save computer resources, the
working data for elevation were resampled to a 30x30 meter resolution. Slope and aspect
derivatives were computed from the 5x5 meter data as these are comparatively small files.
 Size: Lake Tahoe Basin totals 513 sq. mi. in area. At 5 m
2
resolution, this equates to
approximately 266 million pixels.
 Scale: The extent of the dataset covers the Tahoe Basin with 5 sq. meter cells
 Aggregation: The data is continuous; therefore, it is not technically aggregated. The size of
the dataset required it to be resampled into a coarser resolution—a form of aggregation.
 Attributes: These data are expressed in meters (ratio data). Although not specifically an
attribute, the dataset is hydrologically enforced meaning drainages are forced to conform to
known stream features.
 Fuzzy/Crisp: Viewed as ‘point’ data, raster elevation data are crisp; however, the point data
are interpolated into a surface. Any interpolation is an educated guess and is, therefore,
always fuzzy.
33

Figure 6 LTB 5m LIDAR-Derived Digital Elevation Model
(Resampled to 30m Resolution)
This LIDAR-derived Digital Elevation Model was assembled by the San Diego
Supercomputing Center utilizing point cloud data provided by the Tahoe Regional Planning
Agency. The DEM is displayed at its native 5m resolution; however, for analysis, the model
was resampled to 30m to reduce its impact on computer resources. The inset is a slope
derivative of the 5m elevation surface provided to illustrate the granularity of these data. File
sizes for slope and aspect derivatives at 5m resolution are much smaller than the original
elevation surface. Those surfaces were analyzed at their native resolutions.
34
 Error: Vertical error in these data is quantified by root mean square error, which is estimated
at .036 meters for this dataset. While this is an impressive number, LIDAR data have
inherent error. The data reflect the first returns from the LIDAR sensor; this may not be the
ground. The inset panel of Figure 6 illustrates this problem where trees and manmade
objects such as streets and buildings are visible in the image.
Error in this dataset is larger than normal due to the forested terrain of the Tahoe
Basin. Many of the LIDAR returns are likely to be treetops, which can be up to 50 feet tall in
this area. This error is unlikely to present a significant problem for this application. The data
are already aggregated and elevation error of +/–100 m is acceptable given the scale of the
study area.
 Fitness for use: The primary fitness issue with this dataset is its unwieldy size. ArcGIS does
not process extremely large datasets very well, and where it does, processing is lengthy and
places large resource demands on typical personal computers. This is for the raw data—
analysis functions can increase resource demands to the point they may not be possible.
These data (and their derivatives) were resampled into a coarser resolution to decrease
required computer resources.

3.1.4 Tahoe Basin SSURGO Soils Survey
The Soil Survey Geographic Database (SSURGO) is the output from an ongoing nationwide
survey of soils (Figure 7).
35

The data are collected by walking teams that physically survey soils across the country. Their
data are compiled, and soil scientists establish polygons (map units) based on areas with similar
Figure 7 SSURGO Soils Data —Mean Moisture Capacity (cu cm)
The Soil Survey Geographic Database (SSURGO) is an extensive survey of nationwide soil
conditions produced by the US Department of Agriculture’s Natural Resources Conservation
service. The attribute of interest for this research is mean moisture capacity, and a surface
symbolizing it is presented in the figure. Moisture capacity serves as a proxy for overall soil
quality under the assumption that high moisture capacity corresponds to deep soils with upper
horizons that contain ample organic material. The inset illustrates the typical granularity of
these data, although polygon size tends to vary across the study area. The database is
incomplete in one area of the Basin. That area is noted in the figure and, for consistency, all
datasets were trimmed to exclude that area.
36
characteristics. The database is extensive—the metadata document outlining its attributes is
approximately 250 pages long.
 Size: The dataset contains 3,978 discrete polygon objects
 Scale: The extent of the dataset covers the Lake Tahoe Basin that totals 1330 sq. km.
Polygons in the dataset vary from 1698m
2
to 497947729m
2
. The general size of these
polygons is illustrated by the inset of Figure 7.
 Aggregation: These field data are aggregated into polygons. The intent is to keep the map
units uniform, but averaging is inevitable with such a high number of attributes.
 Attributes: The dataset contains hundreds of attributes. In most instances, these are nominal
data that correspond (sometimes literally) to the field notes of data collectors. This analysis
requires ratio or interval data that can represent soil quality in a regression equation. Each
polygon is assigned the weighted average of field-recorded moisture capacity readings (.01
cu cm precision) within the polygon. Moisture capacity correlates to organic content and
nutrients and is used to represent soil quality for analyses. Note that polygons in Figure 7 are
symbolized by their actual values; however, the legend is truncated to five classifications for
brevity.
 Fuzzy/Crisp: These data are undoubtedly fuzzy based on many of the factors previously
discussed. Soils typically merge gradually from one form into another over geographic
space. A notable exception may occur around geologic features such as fault or fracture
zones. These areas can form boundaries of distinctly different geologic formations.
 Error: Error in these data must be regarded as high. Scientists interpret notes from field
workers and establish subjective areal boundaries from afar. The sheer scope of the field
work required to produce this dataset ensures some level of error.
37
 Fitness for use: This dataset is produced by the US Department of Agriculture and is the
national standard for soils data. Still, this is likely the most troublesome dataset involved in
this analysis. One relatively minor problem is that there is a data gap in the northwest section
of the study area (highlighted in Figure 7).

3.1.5 Tahoe Area Weather Stations
A shapefile compiled by the University of Nevada, Reno (UNR) Desert Research Institute
Climate Center containing the geographic positions of weather stations around the LTB that
maintain web-accessible temperature and precipitation data was used in this study (Figure 8).
Location data from the shapefile were joined to a spreadsheet containing mean annual
temperature and precipitation data from each of the stations. These data were imported into a
geodatabase and used to interpolate microclimate surfaces for the LTB.
 Representation: The weather station dataset is a vector point dataset, so the data are discrete.
The interpolated surface is a continuous raster derived from the point precipitation attributes
 Size: The dataset contains 29 discrete points representing mean annual temperature and
precipitation.
 Scale: The extent of the dataset has a minimum bounding rectangle of 1750 sq. miles.
Distances between points range from 1 to 58 miles and average 22.4 miles.
 Aggregation: The point data are not aggregated by area; the climate data were all recorded at
their respective coordinates.
 Attributes: Each point contains two pertinent attributes. Mean annual temperature (time
span varies—see error information) is interval data measured in degrees Fahrenheit and mean
annual precipitation is ratio data measured in inches.
38
 Fuzzy/Crisp The point data are spatially crisp—their exact location is known. The climate
attributes are fuzzy in that they are means that represent a temporal aggregation. Their
values are representative, but they do not indicate a specific point in time.
Error: The attribute error may be significant. First, the historical data do not cover identical
periods of time. Second, the data are collected and reported by differing entities and
methods. Some of the data are volunteered by private individuals, so it is unknown if the
instruments used are professional quality or if the data are accurately reported. Finally, some
stations report summary statistics while others provide a report of daily numbers that may
vary in completeness.
 Fitness for use: The purpose of this dataset is to create interpolated surfaces that represent
microclimates across the Basin. Stations outside the study area were purposely included to
mitigate edge effects. Unfortunately, areas to the south and west lack enough accessible data
caches to produce complete coverage of the study area perimeter. The surface in Figure 8
was created for exploratory purposes using the inverse distance weighted technique. The
resulting surface reflects the expected precipitation pattern with higher precipitation amounts
on the western edge of the LTB and smaller amounts near the Carson Range along the
eastern edge of the Basin.

39

Figure 8 LTB Weather Stations and Preliminary Precipitation Surface
This figure illustrates the location of weather stations whose data were used to compute precipitation and
microclimate surfaces for the Lake Tahoe Basin. Where possible, weather stations located both inside the study
area and around its periphery were used to interpolate the surfaces in order to mitigate edge effects. The colored
surface in the figure is a preliminary surface constructed using the inverse distance weighted interpolation
technique to test the sufficiency of the collected weather station data. The surface generally mirrors the known
climate pattern of the LTB and therefore, the data was deemed adequate for performing a more complex kriging
procedure. Note that the interpolation did not reach the far southern tip of the Basin. This is acceptable given
no land use data is available for this area and all datasets were clipped to exclude this part of the study area.
40
3.1.6 TRPA Land Use and Completed USFS Prescriptions
This dataset delineates land use zones as defined by the Tahoe Regional Planning Agency
(TRPA) as well as areas that received prescribed forest burns or thinning (Figure 9). These data
summarize the varying levels of management intensity around the Basin
 Representation: The dataset is a vector polygon model; the data are discrete.
 Size: The dataset contains 308 discrete polygon objects; however, these data were be
dissolved to combine similar classes such as “backcountry” and “conservation”.
 Scale: The extent of the dataset covers most of the Lake Tahoe Basin with the exception of a
15.5 sq. km. portion of Alpine County for a total of 1313 sq. km. Polygons in the dataset
vary from 6000m
2
to 90 km
2
(wilderness area)
 Aggregation: The polygons represent boundaries assigned by a government agency. They
do not aggregate data.
 Attributes: The key attributes of this dataset are nominal and name the intended land use
within each area. The prescriptive treatment polygons contain nominal attributes that
indicate if the treatment was a thin or a burn.
 Fuzzy/Crisp: These data are truly crisp. They do not represent a natural phenomenon that is
dynamic or loosely defined. The polygon boundaries are exact and will not change unless a
government authority alters them.
 Error: There should be little error in these data because the authority that created them
digitized them. The caveat to this is that the dataset must be properly digitized. Several
polygon slivers were noted while exploring this dataset. A geodatabase topology identified
and corrected those errors.

41

Figure 9 TRPA Land Use and Prescribed Treatments
This figure presents land use designations as assigned by the Tahoe Regional Planning
Agency. These data were consolidated to ease data processing and represent discrete levels
of management impact in the species richness models. Also depicted are specific instances of
prescribed thinning or burning as of the date of data collection. Ultimately, these data were
not included in the species richness models as regression analysis did not indicate they were
a leading factor in predicting species richness. Similar to previous figures, an inset is provided
to indicate typical granularity for these data. Lastly, no land use data for the far southern
Alpine County section of the study area was available. This area was excluded from the
analyses.
42
 Fitness for use: These data provide the spatial extent of forest management technique.
These techniques are reliant on land use, however, many land uses may relate to a given
forest management policy. The data were further aggregated into three zones of management
style, urban, heavy (ordinary forest management) and light (wilderness or conservation
zones).

3.2 Data Processing
The raw data described in section 3.1 were further processed for use in the various analyses
associated with this research. ArcGIS tools were used to manipulate the data. Minor processes
such as creating slope or aspect surfaces are not described. The two major processing tasks were
to create microclimate surfaces and consolidate the data into a single point dataset for
exploratory regression.

3.2.1 Precipitation Surface Creation Using Empirical Bayesian Kriging (EBK)
A fine-grained precipitation surface was required for exploratory regression and as a Maxent
environmental input layer. Empirical Bayesian Kriging (EBK) was used to interpolate this
surface from the UNR Tahoe area weather station data. Kriging is a powerful interpolation
technique, but it requires several data assumptions to create an accurate surface. Specifically, the
interpolated data must be non-clustered, stationary, normally distributed and autocorrelated.
Several diagnostics were utilized to evaluate the weather station data for kriging
suitability (Figure 10). In the top panel, the Voronoi map indicates the data are mostly
stationary. The middle panel is a semivariogram that indicates the data are autocorrelated with a
range of about 15 km. This is expected because weather data are typically autocorrelated. In the
43
bottom panel, the data appear normally distributed with several outliers in the wettest part of the
spectrum. These discrepancies may be attributed to measurement error (i.e. amateur collection
or instrument calibration) coupled with a small sample size.
EBK accounts for uncertainty by simulating many semivariograms. Further, moderate
non-stationarity is tolerated by creating local models within subsets of the data.
The final surface depicts precipitation patterns very well (Figure 11). A visual inspection
indicates that the surface reflects known precipitation patterns in the Tahoe Basin with the
western Sierra Nevada range causing rain shadow and decreased precipitation in the eastern
Basin. An in-depth, quantitative evaluation of the EBK results is presented in Chapter 4.

44

Figure 10 Pre-Kriging Data Analysis (Stationarity, Autocorrelation, Normality)
This figure provides an analysis of mean annual precipitation data gathered from web-
accessible weather stations to measure their compliance with the kriging assumptions of
stationarity, autocorrelation and normality. In all three cases, the data likely meet the
assumptions; however, the figures are not convincing or conclusive given the small sample
size of the precipitation data. Given these diagnostics Empirical Bayesian Kriging (EBK) was
selected to create the precipitation surface. EBK is considered less reliable than traditional
kriging; however, it is more robust to deviation from data assumptions.
45

Figure 11 EBK Precipitation Surface (Inches of Precipitation-Annual Mean)
The final EBK precipitation surface provides an excellent representation of precipitation
patterns in the Tahoe Basin. The Sierra Nevada crest (the Basin’s western border) is highly
effective at stalling northwesterly Pacific storms creating a rain shadow effect across the
Basin. The Carson Range forming the eastern edge of the Basin prevent remaining moisture
from reaching the Great Basin valleys to the east. The surface and point data accurately reflect
these effects.
46
3.2.2 Data Consolidation
TEBVM was converted into a point dataset by calculating the centroid of each polygon and
assigning the associated attributes to it. Interestingly and contrary to species-area theory, these
species richness data do not strongly correlate with area (Arrhenius 1921). An ordinary least
squares regression of species richness to area yielded an adjusted R
2
of only 0.03. Log-Log
transforming the data only marginally improved this value to an R
2
of 0.13. This is not entirely
surprising given the construction of species-area curves requires specific sampling techniques
such as nested transects (Scheiner 2003). These data are intentionally biased; the TBEVM
dataset authors delineated areas by encapsulating homogenous vegetative communities into
polygons. Conversely, sampling techniques designed to construct species-area curves expect to
capture an increasing number of homogenous communities with each widening transect.
(Scheiner 2003).
TEBVM was converted into a point dataset by calculating the centroid of each polygon
and assigning the associated attributes to it. This feature class along with all of the required
raster datasets were placed into a geodatabase along with a copy of the TBEVM centroids
(without attributes). The ArcGIS model builder tool (Figure 12) extracts raster values that
underlie the non-attribute TBEVM “mirror” points and records them as attributes in an
intermediate point dataset. The intermediate points were then spatially joined to the TBEVM
centroid dataset. The output of this tool is a feature class that contains all the TBEVM attributes
plus attributes extracted from the raster datasets. The consolidated dataset was then scrubbed for
null values. These records, representing data gaps in the source datasets were removed to
prevent sampling bias in the various analyses. The final dataset contains approximately 17,000
points.
47

3.2.3 Tree Species Richness Attribute Calculation
TBEVM does not contain a species richness attribute. Several rows from the TBEVM attribute
table (Table 2) illustrate how this value was calculated. Columns in the left portion of the table
represent percent coverage of each tree species in the TBEVM polygons. To calculate tree
species richness, counts of any species coverage other than zero for each row were tabulated and
recorded in the far right column (Tree_specrich).

Figure 12 Data Consolidation Tool (ArcGIS Model Builder)
48

3.2.4 Data Split by Management Intensity
Initial attempts at exploratory regression using the consolidated data set resulted in highly
skewed residuals. Martin-Queller (2011) reported stationary relationships between species
richness and management effects in their GWR analysis. Given this, the consolidated dataset
was split using the ArcGIS split tool according to the categories (Table 3) to account for data
variation by management category.

Land Mgmt. Category Land Use Categories
Urban -Residential
-Tourist
-Resort
-Mixed use
Heavy Mgmt. -Backcountry
-Recreation
Light Mgmt. -Wilderness
-Conservation

3.3 Models and Analyses
This section covers the various models and analyses produced to support this research. They
serve three purposes. First is to derive the most appropriate explanatory variables for species
ABCO ABMA JUOC PIAL PICO PIJE PIMO POTR TSME Tree_specrich
0 0.00543 0 0.2 0.3 0.13 0.12 0 0.09 6
0 0.04 0 0.23 0.13 0.08 0.09 0 0.00455 6
0 0 0 0.1 0 0 0 0 0.01 2
Table 2 Species Richness Calculation
Table 3 Forest Management Categories
49
richness. Second is to produce the species richness border region model itself. Lastly, several
models validate the border region model.
To be clear, the ultimate objective is two final models. The species richness-derived
model (species richness derived from macoenvironmental factors and displayed as border
regions) and the species richness model (traditional Maxent SDMs, stacked and summed to
display species richness). These models validate each other and also provide an opportunity to
evaluate the relative benefits of each approach.

3.3.1 Exploratory Ordinary Least Squares Regression
The ArcGIS exploratory regression tool was used to identify the best specified explanatory
variables for tree species richness in the Lake Tahoe Basin. This technique was chosen as it
provides an efficient method for sorting the numerous potential independent variables identified
in the literature and compiled as attributes in the consolidated point feature class. The primary
limitation of this method is that the ArcGIS tool only considers linear distributions. Non-linear
regressions, such as logistic commonly used to fit ecological data are not supported.
A further complication of using a regression technique in this manner is that the desired
independent variable, tree species richness, are count data with a very small range. Initial
regression attempts using these were fragmented and unsatisfactory.
As a proxy for species richness, the continuous Simpson Diversity Index was calculated
for tree species according to Equation 1 below where ni is the number of individuals of each
species and N is the total number of individuals of all species. The summation is across all
species present (Simpson 1949).

50
TBEVM does not include data for number of individuals; however, estimates were
calculated from the available data. Total area for each polygon was converted to hectares and
the resulting value was reduced to equal the percent of each polygon that contains tree cover.
Total individuals were then estimated by multiplying stem density per ha by hectares of tree
cover. Coverage for each species is represented by percent of total area. A similar process was
conducted for each species present to estimate the number of individuals per species. Clearly,
the true stem density for each species may vary from the polygon means reported by TBEVM.
Consequently, the resulting individual data certainly contains error. Short of conducting an
extensive field survey, however, these data represent the best available estimates.
As mentioned in the previous section, categorical management effects were accounted for
by splitting the dataset and performing separate regressions for each management category.
The exploratory regression tool iteratively performed regressions on combinations of all
the attributes selected from the consolidated dataset. The tool automatically checks for issues
such as multicollinearity and non-normally distributed residuals and then outputs a report
indicating the best performing and best-specified independent variable combinations according
to its statistical diagnostics. Residual plots for the best performing solution were checked for
randomness and normality around the regression model. The independent variables for this
regression model were further evaluated by checking for their use in related literature.

∑ (
𝑛 𝑖 𝑁 )
2

(1)

51
3.3.2 Species Richness-Based Maxent Model
This model is the primary model evaluated by this research. The typical use of the Maxent
software is to input point occurrences of specific species to create a species distribution model
(SDM). For this application, point observations of species richness counts were substituted for
species data to produce predictions of species richness clusters. The goal of the model is to plot
the location and dimensions of border regions separating homogenous patches of species
richness. As mentioned by Kark and van Rensberg (2006), the abruptness of change that occurs
within border zones is also a significant property.
To use Maxent, data that will be input into the application must be pre-processed to meet
strict requirements (Figure 13). Raster environmental layers must be precisely coincident and
cover exactly the same extent. Once coregistered, the raster data must be exported into an ASCII
grid format. Presence-only (species) data are matched with X-Y coordinate data that coincides
with the environmental raster data. These data must be exported into a comma separated value
(csv) format. These tasks were accomplished using the Excel spreadsheet program.
As a black box-type modeling application, the heavy number crunching is done behind
the scenes by Maxent’s internal maximum entropy algorithm. Despite this, a full suite of user
selectable parameters that affect Maxent’s output is available. Some of those option choices and
their rationale are listed below. Specific details regarding the effects of each parameter are as
described by Merow (2013):

52

 Output format —The cumulative output option was be selected given it is designed to
produce crisp range boundaries and avoids using parameters not derived from the input
data
 Feature selection —This selection allows for specifying the regression style for each input
parameter. The specific distribution of each parameter is unknown, so the auto option
was selected which allows Maxent to calculate the appropriate feature type for each input
variable. Note that this relates to the “feature” discussion in Chapter 2. Feature type in
this context relates to the appropriate distribution type of the input environmental data
(e.g. linear, product, logistic, etc.), not the spatial data model involved. All
environmental data are in a raster format.
 Jackknife analysis —Jackknife output was used to verify that each environmental variable
is statistically significant within the model.
Figure 13 Maxent Pre-Processing using AcGIS and Spreadsheet
Applications
53
 Threshold —The threshold setting determines how Maxent evaluates the receiver
operating curve (ROC) to determine if a cell is within or outside the calculated range.
There are a number of possible settings; however, in this case an automated sensitivity
analysis was desired. The equal specificity vs. sensitivity option ensures the output ROC
value is no more sensitive than it is specific. In other words, some accuracy of each
cell’s prediction was sacrificed in order to create a stable (less sensitive to variable
changes) model. Further, choosing a threshold option produces a binary raster (in
addition to the range probability surface) where 1 is range and 0 is not range based the
selected threshold option. This option is beneficial for removing bias as the decision of
what ROC constitutes range is determined by the data as opposed to the user (e.g.
arbitrarily selecting a 0.8 ROC cutoff).
 Regularization—This input allows the user to adjust the magnitude of Maxent’s
complexity penalty. The literature varies on how this option should be approached.
Some advocate a default setting given the Maxent algorithm is highly effective. Others
use an iterative approach to maximize the output kappa statistic similar to the method of
using peak autocorrelation (e.g. Moran’s I) to select an appropriate distance band in other
spatial analyses. In this case this option was varied over several model runs to overcome
Maxent’s tendency to overfit presence data (Figure 14). An overfit model will display
“halos” around presence data, while excessive regularization will be “flat” with little
relief. The chosen models were the best subjective compromise between these extremes.

54

 Test point percentage —To construct model fit diagnostics, Maxent extracts a portion of
the input point occurrences to validate the model. The user is charged with determining
the ratio of test to model training input. There are ~16,000 input occurrence points in the
TBEVM dataset which benefits the model given the Lake Tahoe Basin landscape is
highly varied. The bootstrap sampling method was selected as it is a remove and replace
technique that requires extra processing time because test points used for diagnostics are
subsequently replaced and used to further train the model. Graham and Hijmans (2009)
applied 25% of their presence data for test purposes. This study increased that figure to
30% test vs. training to ensure effective diagnostics, particularly bootstrap output, and to
prevent any training degradation as a result of this high ratio.
 Bias layer —A bias layer is an allowed input to account for sampling bias such as
inaccessible terrain and proximity to roads. This layer was excluded from the analysis
given the presence data are derived from IKONOS remote sensing imagery. Remotely
sensed data provide the advantage of uniform coverage and avoid the inherent field-
collection biases this input is designed to correct (Prates-Clark et al. 2008).
Figure 14 Maxent Iteration
55
Validation of the Maxent output was accomplished via an evaluation against local
knowledge and Maxent’s built-in Area under curve (AUC) diagnostic. AUC measures the
model’s performance versus random by plotting test data, actual ROC and a random prediction.
A value of 0.5 means that the model is predicting ranges as well as a random distribution.
Something less than 0.5 indicates that the model is performing worse than random. Ideally, the
actual ROC curve should peak in the upper left corner of the plot. A value of 0.7 is considered
adequate for most applications (Graham and Hijmans, 2006). An evaluation against local
knowledge also verified that richness predictions coincided with expected output. For instance,
sub-alpine regions ordinarily harbor only two of the represented species. High elevation areas
were checked for consistency with that knowledge.
To create a representation of border regions, Maxent species richness predictions were
post-processed in ArcGIS (Figure 15). Choosing a threshold option in Maxent produces binary
“range” or “not-range” rasters for each species richness value (8 total). Pixel values of “1”
representing predicted range were reclassified to their respective species richness values. Next,
the ArcGIS raster to polygon tool was used to create vector polygons that cover the extents of
each species richness range. These polygons were then intersected to create a vector polygon
layer that represents only those portions of the study area where species ranges overlap. This
vector layer was used as a mask to extract values from each reclassified raster layer. This
procedure trims the reclassified range rasters so that only pixels that Maxent classified as range
for two or more species richness values are represented (i.e. border regions).
56

A benefit of using species richness as a Maxent species is that species richness categories
are actually meaningful values. This property makes the abruptness of a border calculable by
subtraction. For example, a border separating 6 species from a community of 2 species is much
more abrupt than a possibly imperceptible shift from 3 to 4 species.
The abrubtness value was extracted by stacking and subtracting the trimmed and
reclassified range rasters. This was done iteratively to create a series of difference layers
(e.g. 1–8 species, 2–8 species, 3–8 species. . .). The maximum difference value for each pixel
was then extracted and displayed. The resulting layer is a depiction of transition zones between
homogenous islands of species richness classified by abruptness.

3.3.3 Species Range-Based Maxent Model
The stated purpose of Maxent is to predict the ranges of specific species. Given this, an
additional model deriving species richness data from single species range predictions was
constructed—a stacked SDM (Figure 16). If predictions are significantly similar between the
two models, the validity of predicting species richness with Maxent is enhanced. Note that this
Figure 15 Post Processing —Species Richness Method (ArcGIS)
57
method does not specifically address border regions as does the species-richness based model.
This is beneficial as it serves to illustrate how patterns differ between a full representation of
species richness versus border regions only.

Pre-processing and Maxent options are identical to the species richness technique. Post-
processing differs in that species richness is calculated by summing number of species predicted
to occupy each pixel. Pixels valued one in the resulting surface are reclassified to zero to reduce
clutter on the surface and deemphasize areas with little or no diversity.

3.3.4 Known Species Location Versus Predicted Species Range Map
While Maxent is widely regarded as a valid tool for creating SDMs, the output of any model
must still be validated; therefore, a known species location overlay was used to validate the
Maxent output for each individual species (i.e. the individual layers stacked and summed to
create a species richness model). For each species, TBEVM points where that species exists
were overlaid onto its SDM. Ideally, these points will fall within the extent of Maxent range
predictions.
If the Maxent species ranges coincide with TBEVM dominant species, the credibility of
the Maxent prediction is enhanced.

Figure 16 Post-Processing--Species Range Technique (ArcGIS)
58
3.3.5 Split Moving Window Dissimilarity Analysis (SMWDA)
The final validation model to support this research is an SMWDA analysis of the species
richness boundary zones identified in the Lake Tahoe Basin using the modeling technique. The
specific purpose of this analysis is to verify that the plotted boundary zones meaningfully
represent a transition between species richness patches rather than mere variance in the
predictive power of Maxent.
Hennenberg (2005) discusses several quantitative techniques for detecting borders and
ecotones. Most of these, however, are multivariate. SMWDA as presented by Cornelius and
Reynolds (1991) was selected for two reasons. First it is valid for univariate (and multivariate)
analyses. Univariate analysis is desired for this application because it will isolate discontinuities
in species richness only, eliminating ambiguity in the results. Second, while it is a moderately
complex iterative procedure, its mathematics consist of common statistical concepts no more
complex than summations, means and z-scores. Importantly, it does not require specialized
computer applications or programming. It is computable with a carefully constructed
spreadsheet.
The method described by Cornelius and Reynolds places a window along a series of
ordered data (e.g. a transect). The window is split into two halves and averages for the
variable(s) are calculated for each half. An index of dissimilarity is calculated to quantify the
dissimilarity between the window sections. The window is shifted one plot and the procedure is
repeated for the entire series. The expected mean and standard deviation are determined via a
Monte Carlo procedure (1000 random iterations in this case). Z-scores for the dissimilarity
index within the data are calculated and plotted. Significant z-score spikes indicate the presence
of discontinuities in the data (interpreted as the presence of a border or ecotone). The scale at
59
which discontinuities occur can be detected by varying the size of the window. The specific
mathematics are described by equations 2 through 7 below.
For this application, a series of TBEVM centroids that pierce or pass through plotted
transition zones were extracted for analysis. If the plotted border regions represent true
transition zones, discontinuities in the plotted z-scores (peaks) should correspond with the
model-predicted border regions.
The primary issue with this technique is that the TBEVM plots are not evenly distributed
as in field collected transects using evenly spaced quadrats along a compass bearing. This only
invalidates the technique of varying window size to estimate scale given the number of plots
along the data series will not correlate to a consistent Euclidean distance. There will likely also
be some distortion in the shape of curves formed by a series of varying dissimilarity scores. This
is inconvenient, but not fatal as the primary objective is to compare peaks with their associated
window midpoint.
Chapter 4 presents the results of these analyses.

60

Where (for univariate analysis):
j = the data value i = the position in the sequence
Q = window width Q/2=total positions per half (even number)
k= sequential position (Q/2, Q/2+1, Q/2 +2…) Wa=series half 1
k+0.5=window midpoint Wb=series half 2
N= series length v=number of measured variables (=1)
Xij=i at point j N-Q=total windows of width Q
DRk+0.05,i=array of dissimilarities M=Monte Carlo iterations (=1000)

Upper Window Average
𝑊 ̅
𝐴𝑘 +0.5𝑖 =
∑ 𝑋 𝑖𝑗
𝑘 𝑗 =𝑘 −𝑄 /2
𝑄 /2

(1)
Lower Window Average
𝑊 ̅
𝐵𝑘 +0.5,𝑖 =
∑ 𝑋 𝑖𝑗
𝑘 +𝑄 /2
𝑗 =𝑘 +1
𝑄 /2

(2)
Dissimilarity Index
𝐷𝑆
𝑘 +.05
= [∑(𝑊 ̅
𝐴𝑘 +0.5,𝑖 − 𝑊 ̅
𝐵𝑘 +0.5,𝑖 )
2
𝑣 𝑗 =𝑙 ]
1/2

(3)
Mean Dissimilarity
(for Monte Carlo)
𝐷𝑆
̅ ̅ ̅ ̅
𝑘 +.05
=
∑ 𝐷𝑅
𝑘 +0.5,𝑙 𝑀 𝑙 =1
𝑀
(4)
Std. Deviation of Dissimilarity
(for Monte Carlo)
𝑆𝐷
𝑘 +0.5
=
[∑ (𝐷𝑅
𝐴𝑘 +0.5,𝑖 − 𝐷𝑆
̅ ̅ ̅ ̅
𝐵𝑘 +0.5,𝑖 )
2
𝑀 𝑙 =1
]
1/2
𝑀 − 1
(5)
Dissimilarity Z-Score
(Univariate Only)
𝐷𝑍
𝑘 +0.05
=
𝐷𝑆
𝑘 +.05
𝑆𝐷
𝑘 +0.5

(6)

61
CHAPTER 4: RESULTS
This chapter consolidates the results from each of the analyses described in Chapter 3.
Traditionally, scientific papers present results without commentary. Due to the highly graphic
nature of spatial analyses, this chapter departs from that paradigm for the convenience of the
reader. In cases where reference to the details of a figure aids the discussion, a brief
interpretation follows the description of each figure. Broad-scale discussion and conclusions are
reserved for Chapter 5. This strategy is not intended to discourage alternative interpretations or
dissent; rather, the specific purpose is to provide easy reference to figures as they are discussed.
Results are not necessarily presented in the order they were produced. The subsections of
this chapter are arranged to proceed logically toward the conclusions presented in Chapter 5.

4.1 Evaluation of EBK-Derived Precipitation Surface
The EBK-derived precipitation surface is an important input to both the OLS procedure and
Maxent models in this thesis. As such, the resulting figure was carefully evaluated for
performance and accuracy.
Parameters for the algorithm were set to optimize semivariogram fit and performance.
Specifically, the thin plate semivariogram model with four sectors rotated to capture regions of
significant variation was selected. No data transformation was chosen as none improved the
model’s fit to the data.
These parameters were adjusted dynamically in response to diagnostics within the ArcGIS EBK
application. The final diagnostic output is displayed below (Figure 17). The top panel is the
semivariogram used by the interpolator. Ideally, the blue semivariance averages should fit
within the purple confidence envelope near the model function. The model performs relatively
62
well at short distances and significantly worse as distance increases. This is acceptable given
weather stations were selected to provide many short distance data pairs near the study area.

The bottom panel is the standardized error plot for the model. The residuals appear
widely scattered and follow the model indicating reasonable performance.
Figure 17 EBK Diagnostics (Model Fit and Residuals)
These diagnostics evaluate the output of the kriging operation for mean annual precipitation.
The top panel is the semivariogram produced by the kriging algorithm. Ideally, the blue
crosses should fall within the dashed confidence interval. The results indicate an imperfect
fit particularly at long distances; however, error at long distances is irrelevant given data
outside the study area was included to combat edge effects. The bottom panel represents error
versus fits. The results exhibit the desired shotgun-style pattern, and generally follows the
model although there are several outliers in the dataset.
63
The quality of the kriging interpolation varies across space, and thus, prediction quality
may be quantified using standard error. For the LTB precipitation surface, spatial distribution of
this error was displayed as a validation surface (Figure 18). The lowest standard error values are
centered on the study area due to favorable weather station distribution. Notably there are areas
of higher error along the western study area fringe and in the extreme southern portion of the
Basin. There are few web-accessible weather stations surrounding those (largely wilderness)
areas, creating a data gap. Further, the surface does not reach the southern tip of the Basin. This
is acceptable as this area (Alpine County) also lacks land use data. For data consistency, the far
southern tip of the LTB was excluded from each of the models and analyses in this project.
64

Figure 18 Precipitation Surface Prediction Standard Error
Prediction Standard Error provides a spatial estimation of the quality of .a kriging prediction. In this
figure, the majority of the study area is predicted to have low error although there are areas of concern.
Specifically portions of the northwestern and western edges of the study area are predicted to have
substantial error relative to the rest of the Basin. This is unavoidable due to a lack of accessible
climate data in these areas. The far southern tip of the LTB also has considerable error, although that
portion of the Basin is largely excluded from the analyses. Weather station data are included to
illustrate the rate of confidence decay from known data points. Tight radii around data points suggest
an overfit prediction; however, given the varied terrain of the LTB, tight predictions are preferred
versus predictions for a flat, homogenous landscape.
65
4.2 Selection of Environmental Variables
Ordinary least squares regression analysis was performed to identify a global model that best
describes species richness around the Basin and choose the most appropriate environmental
variables for inclusion in the Maxent models. An initial exploration of 14 potential explanatory
variables (identified in the literature) was undertaken using the ArcGIS Exploratory Regression
tool. The Simpson Diversity Index was used as a continuous proxy for species richness and the
dependent variable for the regression analysis.
Several high R
2
model combinations were returned, but no model was properly specified
due to skewed (Jarque-Bera statistic p<.05) or autocorrelated (Morans I statistic p<.05) residuals.
Variables with coefficients that scored as significant for less than 95% of the model
combinations were discarded. Value distribution histograms for the remaining variables were
examined and most were not normally distributed. The majority of the significant variables
mirror the variables used by Martin-Queller (2011) and discussed in DeClerck et al. (2006) and
Adams (2009). These factors (Table 4) were transformed to better approximate a normal
distribution and meet the assumptions of OLS regression.

66
Table 4 Environmental Variables Selected from Exploratory Regression

Although the selected variables were highly significant, the misspecification of the model
due to significant Jarque-Bera and Moran is I statistics was concerning. The model was
troubleshot by including factors (individuals data) used to compute the dependent variable
(Simpson Diversity Index) with the array of selected variables. The assumption was
incorporating factors used to compute the dependent variable along with extremely significant
environmental factors provided the best opportunity to produce a good fitting model. This was
not the case statistically. Again, the best specified models had high R
2
values (~0.71), but each
failed for skewed and autocorrelated residuals. Given these results, it is unlikely that a perfectly
specified global model (using statistical diagnostics) is possible with these data (due to non-
linearity or excessive outliers).
Variable Transformation (for
OLS)
Discussed in literature? Eco Significance
Basal Area Log Y (Adams, DeClerck) The area of ground
physically occupied by
trees. An important
measure of productivity
and also human
disturbance
(cutting/fires/thinning =
less BA)
Soils (Moisture
Capacity)
Log Y (Adams) Source of
nutrients/competitive
resource
Slope Log N Niche delineator
Elevation Log Y Adams, Martin Queller) Niche delineator-defines
biome/community
separation
Precipitation Mean Difference Y (DeClerck) Moisture/Snowfall define
niches and is competitive
resource
Aspect None Y (Adams, Martin
Queller)
Defines available
photosynthetic energy
(sunlight)
Stream
Environment
Log N Local riparian
communities are
structured significantly
different than other
communities
67
Due to these results, the data were split according to management intensity (as described
in Chapter 3) and reanalyzed using the ArcGIS OLS tool. The statistical results indicated
improved significance; yet, remained misspecified for residual normality and autocorrelation
(Table 5). A manual examination of the OLS residuals was accomplished to evaluate if the
model was usable despite its statistical misspecification.

Management Area Adj. R
2
AICc Koenker BP Jarque-Bera Morans I
Urban .741 22104 .000 .000 .000
Light Management .711 52709 .000 .000 .000
Heavy Management .681 25829 .000 .000 .000

Ecological data are inherently noisy and typically contain significant numbers of outliers,
so R
2
values are rarely higher than ~0.75-0.80. This is reflected in the literature. Bocard et al.
(1992) attempted to partition variation in ecological data across several ecosystems ranging in
scale from bacteria to boreal forests. Despite sophisticated procedures, they found 61% of their
forestry data variation was unexplained due to the natural complexity of biotic and abiotic
explanatory variables. Given that, these models are performing reasonably. AICc for light
management is high compared to the other models, however. More concerning are the
significant JarqueBera and Moran’s I figures. Histograms of residuals (Figure 19) indicate that
the residuals are closer to normally distributed than the statistics would imply.
Table 5 Statistical Diagnostics Following OLS
68

Urban
Light
Mgmt
Heavy
Mgmt
Figure 19 OLS Residuals —Histograms and Scatter Plots
Histograms and scatter plots graphically depict the goodness of fit of Simpson Diversity Index
data to the ordinary least squares regression models. The histograms indicate the distribution
of residuals around the model. Ideally, the residuals should be normally distributed around
the model. That is, the distance of most data points from the model’s prediction should be
small and the volume of residuals should decrease as distance increases. The scatter plots
depict the distance in standard deviations each residual is from the prediction. For these
ecological data, known data within two standard deviations of the predicted value is
considered a good fit.
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The distributions are somewhat leptokurtic, with more residuals gathered around the
mean than expected. Leptokurtic distributions such as LaPlace and Student’s T tend to have fat
tails and this is reflected in the histograms (Zar, 2010). All three scatter plots have residuals

clustered within two standard deviations of the mean. In all likelihood this represents the natural
variance of the system. Several significant clusters sit outside the 2 standard deviation plane
along with a large number of outliers. Residuals from the models were recombined into a figure
that depicts the location of data points that fall more than two standard deviations from the model
(Figure 20).
Figure 20 Geographic Distribution of OLS Residuals (Over and Under
Prediction —Fits Within 2 Standard Deviations)
This study accepts residuals within two standard deviations of the model prediction as a good fit.
Not every prediction fits that criterion; therefore, it is useful to examine how poor fits are spatially
distributed. It appears from this figure that most of the LTB acceptably fits the diversity regression
model. There are clusters of ill-fitting data points that warrant further examination; however, for
the purposes of this study, the diversity model encompasses an acceptable percentage of the Basin.
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Red and green areas highlight the geographical locations where the model over and under
predicts, respectively. The grey area in the southern portion of the figure represents an area of
incomplete data. Data from that region of the study area was not included in the model. Clearly,
the model is not perfectly specified. If a natural two standard deviation variance is accepted,
however, the model adequately describes diversity across the majority of the LTB.
Rykiel (1996) investigated the validation of ecological models. In part, he asserts that
models can be validated outside traditional statistics. One of his key points is that models can be
validated for pragmatic purposes given that they are credible. In this case, heavy credibility for
these models lies in the fact that the explanatory variables have been used for identical purposes
in the peer-reviewed literature. Given this and the high model fit rate illustrated in Figure 20,
these models were deemed credible enough to be used as the environmental factors in the
maximum entropy analysis in this research.

4.3 Maxent Models
Maxent models designed to predict species richness are the primary elements under study by this
research. Two models were produced: the primary species richness-based model and an
individual species range-based model, produced primarily for validation purposes. The models
were created using the parameters and procedures described in Chapter 3. This section begins
with a brief discussion of issues common to both procedures and continues to the specific results
and diagnostics for each model. Finally, the two models are compared for evaluation purposes.
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4.3.1 Common Procedural Issues
With appropriate presence data (TBEVM tree species and species richness) and environmental
layers in hand, the modeling process moved to the Maxent processing stage as described in
Chapter 3.
In every species richness case, several runs were necessary for two primary reasons.
First, the Maxent models are stochastic, so each run is likely to result in slightly different results.
Second, as mentioned in the methods chapter, Maxent has a literature-noted propensity for
overfitting models. The fix for that issue is to examine individual model runs and adjust the
regularization output to apply a complexity penalty that “loosens” the model output.
For each species richness case, Maxent was run three times at the default regularization
to evaluate consistency in the model. Each run involved up to 500 training iterations (the default
maximum). The specific number of iterations for any run is an internal Maxent function. In
every case, the resulting predictions surfaces were similar, but the initial runs (at default
regularization) appeared overfit. This is a subjective measurement; however, the jackknife
diagnostic output was used to apply a measure of quantification to this issue. Specifically, the
jackknife bar graph for many initial runs indicated that every environmental input had an equally
high influence on the model output. Further, the graphical range output in overfit runs appeared
to hug the input presence data and exclude legitimate probable range in favor of known presence
data. The regularization was iteratively increased until full, stable (i.e. consistent results over
three runs) coverage was achieved.

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4.3.2 Species Range-Based Model
The species range-based model was created as a method of validation for the species richness-
based model; it is presented first because it proved to be the less effective model (Figure 21).
An initial check of the model, based on local knowledge, indicates that the predicted
species occurrence probabilities are reasonable. For instance, white bark pine (Pinus albicaulis)
is a high elevation species native to the sub-alpine biome. Zones of predicted white bark pine
range indeed occur in patches along mountain crests.
Known points of species presence (from TBEVM) were then overlaid onto the Maxent
“thresholded” (binary) range model (Figure 22). When a threshold parameter is selected in
Maxent, the package uses the selected technique to make a best guess of which probabilities
constitute a species’ range and which do not. This may be a user-selected probability, but in this
case, the “equal sensitivity and specificity” function was selected to eliminate bias.
Ideally, known, real world species locations should directly correspond with their
predicted ranges. The results were mixed. For white bark pine, the results were excellent. Other
SDMs, such as for red fir (Abies magnifica) and white fir (Abies concolor) performed much less
consistently.
These inaccuracies should probably be expected. The environmental variables used to
predict each species range are the same factors that were used to predict ranges of species
richness. In other words, environmental factors were selected via research and analysis to
predict general diversity, not each individual species. Defining a tailored suite of environmental
variables for each species would extend far beyond the scope of this research. Individual species
across the spectrum of flora and fauna tend to establish ranges based on specific niches. In some

73

Figure 21 Maxent SDMs for Tree Species Lake Tahoe Basin, CA/NV
Maxent Species Distribution Models (SDM) for tree species in the Lake Tahoe Basin are
illustrated. For consistency and convenience, each SDM utilized the same general diversity
environmental variables used in the species richness models. Red areas of the surface indicate
a high likelihood of habitat for each species; whereas, green areas indicate a low habitat
probability.
74

Figure 22 LTB Maxent SDMs (binary) with Species Presence Overlay
Green areas in this figure are Maxent’s best estimates of each species’ range Unlike Figure
21, this is a binary “range” or “not range” representation as opposed to a probability
continuum.. Small x symbols represent locations of known species presence. The best
performing SDMs coincide with these presence data.
75
cases these align well with diversity factors such as elevation or soil quality. In other cases
specific factors such as canopy cover (i.e., shade tolerance) be involved.
On the surface, the species range technique for predicting species richness appears more
straightforward in a technical sense; however, a detailed evaluation of the pertinent
environmental factors affecting each niche would be required for fine accuracy work.
While there are accuracy questions with some of the species range predictions, the
general patterns are sufficiently correct to provide a reasonable validation device for the species
richness prediction method. Most notably, in nearly every case, a species presence data point
occurs where a species range is predicted; although in some cases there are very few (e.g. white
fir).
A final stacked SDM surface (Figure 23) consolidates each SDM into a validation
surface. Note that species richness border regions cannot be isolated using the stacked SDM
technique, although in many cases they are visible. The stacked SDM model is a true species
richness surface. Its validation function is to compare its species richness patterns with those
produced by the species richness-based method and displayed as border regions (they should be
similar if both techniques are valid).
Notable features in the stacked SDM model include the density of richness ranges in the
wilderness areas (set off by insets). Although it will not be explored by this research, these
dense regions could represent areas of shifting mosaic-steady state. The bottom inset highlights
an area of urban-wildland interface. The primary feature of interest is a line of red-orange
patches of high species richness along the interface.
76

Figure 23 Maxent Species Richness Regions —Species Range Method Lake
Tahoe Basin CA/NV
This figure is the result of summing the total number of species ranges that cover each pixel.
The result is a species richness surface. Border regions appear as areas of extremely high
diversity. They are areas that incorporate species from multiple homogenous zones of species
richness. Areas where this is apparent are magnified by insets. Management level is also
incorporated into the figure to illustrate portions of the study area where species richness
follows management style.
77
This area of high diversity is likely an area of overlap between species ranges to the left
(2–3 species) and the right (5–6 species)—a border region. This north-south string of abrupt
border regions reflects a known zone of species richness change between adjacent woodland and
urban zones (the airport in this case).
Finally, regions of management intensity are depicted on the map. In many areas, patterns
of species richness align with these zones indicating a possible link between species richness and
management style and/or intensity.

4.3.3 Species Richness-Based Model
The species richness-based model is the primary model being investigated for credibility and
utility by this research. Similar to the model presented in section 4.2.2., the model was
constructed using the stepwise procedure described in Chapter 3. A critical intermediate step in
producing the species richness-based model is to use Maxent to predict species richness. Given
the validity of these predictions represent one of the major research questions addressed by this
thesis, emphasis is placed on statistical diagnostics bundled with the Maxent predictions.
Specifically, the results of Area Under the Curve (AUC) and jackknife analyses are presented to
bolster the credibility of using Maxent to predict homogenous regions of tree species richness.
The range probability output for tree species richness values in the LTB (Figure 24) provides for
an initial evaluation. As a first step, the output ranges were examined against local knowledge
similar to the process used for the individual species ranges in Figures 21 and 22. The ranges
make sense. For instance, the ‘1’ species range indicates high range probability at the Basin’s
highest elevations. This makes good-sense given that the high elevation sub-alpine zone
generally hosts a limited number of hearty, long-lived tree species such as white bark pine.
78

Figure 24 Maxent Tree Species Richness Distribution Models
Lake Tahoe Basin CA/NV
This figure presents the Maxent distribution models for tree species richness. Typically,
Maxent output predicts the likelihood a pixel is habitat for an individual species by combining
species presence data with relevant environmental factors. These models substitute species
richness observations for species presence and incorporate factors that contribute to tree
diversity in the LTB. The models do not predict any particular species. Rather, the models
predict the likelihood a specific number of species will exist within in a particular pixel.
79
The ‘8’ species zone incorporates an area of the Basin where there is evidence of
succession from sun-loving Jeffery pine to fir species whose recruits better tolerate the dense,
shady understory of forests that have been actively fire-suppressed for decades (Taylor et. al.
2014).
The primary statistical check of each SDM was an evaluation of Area Under the Curve
(AUC) (Figure 25). The curves being referenced are the Receiver Operating Curve (ROC) and
the associated curve of test values (randomly chosen data points from the input presence-only
data). In each graph, the red curves represent ROC, the blue curves represent test data and the
grey lines are a reference random prediction.
ROC is the probability that a cell contains a species richness value versus the rest of the
background cells. Where the blue line closely matches the red line, the model is performing well
as predictions are closely following the test data.
The axes of each chart represent specificity (x) versus sensitivity (y). Precisely how
Maxent calculates ROC (and hence separates range from not range) is adjustable by the user. As
a safeguard against a biased or invalid (due to excessive sensitivity), Maxent was set to equalize
sensitivity versus specificity. The Maxent prediction algorithm adjusts or omits predictor
variables and checks for excessive change in the final range predictions. Maxent adjusts the
threshold until the output values are no more sensitive than they are specific
Each of the final eight species richness predictions met the 0.7 AUC benchmark and their
test data closely mirrored the ROC plot. Creating eight comparable (i.e. use the same input
variables) that are also statistically well-specified is challenging. That each of the models
surpassed the established benchmark is a strong argument for their validity.

80

Figure 25 Maxent Area Under Curve (AUC) Analyses for LTB Tree Species
Richness Distribution Models
The AUC charts plot specificity (x) vs. sensitivity (y). 0.5 AUC is considered a random
prediction. 0.7 considered an adequate prediction. Ideal curves peak in upper left corner.
81
It must be noted that accurate Maxent predictions are highly dependent on the careful
selection of environmental variables. While great care was taken to select the most relevant
variables via literature research and regression analysis, the Maxent jackknife analysis provides
an excellent final verification that each of the selected environmental elements indeed
meaningfully impacts the SDM. A representative sample of the analysis (Figure 26) for three

species (the full set appears in Appendix 1) is presented here. The dark blue lines indicate that
each variable is significant (not left of the y-axis) and that their influence varies. The more right
the blue line, the greater its influence on the model. While this graphic is highly representative,
the specific contribution of each variable differed from model to model. Not surprisingly,
elevation is most consistently significant across all the species richness SDMs, given elevation is
the primary determinant of biome in the LTB. Basal area is also a consistently significant
variable although its influence diminishes as species richness increases.
This is consistent with basal area’s function as a “wildcard.” It captures many of the
unspecified noise variables in the system that produce a significant effect, but cannot be captured
in a global variable due to their infrequency (e.g. disease, insect infestation or discrete
Figure 26 Jacknife Analysis for 3 Species
82
management events). Very diverse forests likely experience fewer of these random disturbances,
hence basal area’s generally inverse relationship with species richness.
The light blue bars quantify the effect of eliminating a variable from the model. For each
variable, the further its bar reaches to the left, the heavier its omission affects the SDM. That is,
leaving a variable out will significantly change the prediction.
An additional important result is the decision to omit an SDM for zero species from the
modeling process. The SDM for zero species (Figure 27) suggests that, with few

Figure 27 Tree Species Richness Distribution Model for Zero Species:
Raw Maxent Output for Lake Tahoe Basin CA/NV
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exceptions, suitable conditions for zero tree species can occur throughout the study area. This is
a reasonable prediction. Rocky outcrops and treeless meadows are common across the LTB;
however, the high uniformity of these data make them more apt to contribute noise than
information to the models.
Beyond their specific utility, the validity of these zero species data is questionable due to
the mechanics of Maxent itself. As a presence-only algorithm, is it reasonable for it to predict
the 'presence' of nothing? This is an interesting question, but it certainly exceeds the scope of
this investigation.
Conceivably, these data could produce a more complete model. Their potential for
contributing noise along with their questionable validity, however, were deemed to outweigh
their potential benefit, so they were omitted.
The final species richness border region output produced by this model provides a clean
depiction of species richness patterns in the LTB (Figure 28). Note that border regions with the
lowest abruptness value (1 species) were assigned no value as these likely represent the most
uncertainty in the model, are least interesting and tend to clutter the figure.
The model’s most notable features mirror the features highlighted in Figure 23. The
bottom inset isolates an instance of wildland/urban interface near South Lake Tahoe, CA. This
model identifies this known, highly abrupt zone of species richness change very clearly.
Portions of the Desolation and Mount Rose Wilderness areas are also inset. Wilderness
ecosystems are left to regulate themselves barring extreme circumstances. The myriad of species
richness zones could support the theoretical shifting mosaic/steady state pattern, while urban and
more heavily managed areas appear to have a more uniform species richness pattern.
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Figure 28 Maxent Derived Tree Species Richness Border Regions —Species Richness
Method: Lake Tahoe Basin CA/NV
Final species richness surface proposed by this research. Border regions are classified by
abruptness indicating the relative differences in species richness each border region
represents. Insets highlight areas of the Basin where species richness patterns are dense. The
Urban-wildland interface inset highlights an instance of species richness change known to be
extremely abrubt (forested landscape abutting the clearcut airport area). Zones of
management style are included to provide a visualization of management effects on diversity.
85
4.3.4 Validation of Species Richness Models by Comparison
For the purpose of comparing the two surfaces, the species richness-based and species range-
based models are displayed side by side (Figure 29). As mentioned previously, the purpose of
the species range-based (stacked SDM) model is to validate the species richness-based (border
region) model. Specifically, the primary element that requires additional credibility is the use of
Maxent to predict regions of species richness.
The underlying basis for this validation is that the validity of Maxent for the purpose of
predicting individual species ranges is widely accepted in the literature. This is not the case for
predicting species richness. If the two models, using identical environmental and presence data,
and independent procedures designed to utilize Maxent species richness and species range data,
respectively, arrive at significantly similar output, the credibility of using Maxent to predict
species richness is greatly enhanced.
The earlier comparison of tree species SDMs versus known locations of respective
species revealed some accuracy issues (likely due to choice of environmental variables);
however, the general patterns were deemed acceptably accurate. Despite this limitation, the
patterns displayed by the two models are extremely similar.
Note that the two models do not present identical information. The stacked SDM model
presents homogenous zones of total species richness, while the species richness-derived model
presents border regions classified by abruptness. The important observation is that the overall
diversity patterns presented in the two models are extremely similar across the study area. This
confirms that Maxent is predicting the same patterns using different approaches.

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Figure 29 Model Comparison: Tree Species Richness Models —Species
Range Method (top) vs. Species Richness Method (bottom)
This figure facilitates a visual comparison of the models produced by this research. The
models support the validity of Maxent species richness models given they are functionally
equivalent surfaces produced via different techniques. Both models effectively represent
LTB tree species richness patterns although their specific representations differ.

Figure 100 Model Comparison: Tree Species Richness Models—
Species Range Method (top) vs. Species Richness Method (bottom)

Figure 101 Model Comparison: Tree Species Richness Models —Species
Range Method (top) vs. Species Richness Method (bottom)

Figure 102 Model Comparison: Tree Species Richness Models—
Species Range Method (top) vs. Species Richness Method (bottom)

Figure 103 Model Comparison: Tree Species Richness Models—
Species Range Method (top) vs. Species Richness Method (bottom)

Figure 104 Model Comparison: Tree Species Richness Models —Species
Range Method (top) vs. Species Richness Method (bottom)

Figure 105 Model Comparison: Tree Species Richness Models —Species
Range Method (top) vs. Species Richness Method (bottom)

Figure 106 Model Comparison: Tree Species Richness Models —Species
Range Method (top) vs. Species Richness Method (bottom)

Figure 107 Model Comparison: Tree Species Richness Models—
Species Range Method (top) vs. Species Richness Method (bottom)

Figure 108 Model Comparison: Tree Species Richness Models—
Species Range Method (top) vs. Species Richness Method (bottom)

Figure 109 Model Comparison: Tree Species Richness Models —Species
Range Method (top) vs. Species Richness Method (bottom)
Species Richness Surface —Stacked SDM Species Richness Border Region Surface —
Macroenvironmental Prediction
87
The detailed insets provide more a fine-grained comparison of species richness patterns.
The wildland-urban interface is quite visible in both models as dark red or orange patches. In the
stacked SDM model, these patches relate to high species richness resulting from overlapping
ranges. Note that these are generally bordered by yellow-orange areas of less richness.
Conversely, the same area in the border region model contains isolated red patches representing
very abrupt areas of transition—border regions. The relative isolation of these patches in an area
of known richness change indicates that border regions were successfully isolated and displayed.
Similar patterns are evident within the wilderness area insets. Dense mosaics of species
richness are evident in the within the stacked SDM model and the border region model outlines
them well.
In sum, these models are functionally equivalent in that they represent the same diversity
patterns. Their differences allow for studying them in different ways. In particular, the border
region model provides an opportunity to investigate species richness in a new and interesting
way.

4.4 Split Moving Window Dissimilarities
The species richness-based model depicts the border regions that divide homogenous plots of
tree species richness. These are defined by portions of the Maxent predicted species richness
ranges that overlap. These regions potentially define a class of spatial entity that is not described
elsewhere in the literature. The purpose of SMWDA in the context of this research is to establish
that these border regions are detectable entities and not simply variance in the predictive power
of the Maxent algorithm.
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Border and ecotone researchers consider SMWDA z-score peaks to be evidence of
borders or ecotones. For this application, the principle idea is that if species richness border
regions represent legitimate ecotone-like entities, they should be detectable using SMWDA.
The sampling area chosen for SMWDA analysis is in the northern portion of the LTB
(Figure 30). This area was selected because it encompasses a large number of predicted border
regions and as well as areas of significantly homogenous species richness (i.e. gray area).
Further, the sampled zone spans a wilderness area, a developed recreation area and non-
wilderness primitive area. Lastly, the sampling zone contains a large sample of TBEVM data
(74 data points) for analysis.

Figure 30 SMWDA Sampling Location North Lake Tahoe, CA/NV
The red rectangle represents the location of species richness data that were extracted from the
TBEVM dataset for analysis using SMWDA. The location, size and shape of the sampling
area were chosen to encompass a sufficient sample size of data points, approximate a linear
dataset and capture a large number of border region predictions.
89
The results of the analysis (Figure 31) are moderately conclusive. As mentioned in a
previous chapter, species richness is very sensitive to scale. Varying the window size used in
SMWDA analysis fine tunes the scale of the analysis. Several iterations of SMWDA were
conducted on these data with window sizes ranging from four to ten data points. As expected, no
scale perfectly captured every border region; however, a six data point window reflected the
expected pattern very well. For reference, a Monte Carlo simulation predicted that across the
entire transect, the expected species richness change for any six point window is 2.1 species.
The z-score for each point represents how many standard deviations from expected its six point
window is. Note that for clarity (and reference to the related map), a z-score is plotted for each
data point although this is not precisely accurate. Each window necessarily contains an even
number of data points so that it may be split into even halve. The z-score relates to the midpoint
of each window which is midway between the third and fourth points in this case. For example,
the results graph in Figure 31 begins with data point number 3 representing the first position of
the six point moving window. Strictly speaking, the related z-score refers to a geographic point
between data point 3 and 4. The next window position (represented by data point 4) refers to a
point between data points 4 and 5 and so on.
A precise geographic representation of each SMWDA z-score is unimportant given the
data restrictions of this analysis. SMWDA performs best using field collected transect data
where the data are evenly spaced. Practical limitations precluded field collection of samples for
this analysis. The TBEVM species richness data used for this analysis is not specifically linear
nor are the data evenly spaced. This skews the z-score spread and geographic relationship
between the results graph and the dataset. These are relatively minor issues, but must be kept in
mind during interpretation of the analysis.
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Figure 31 Split Moving Window Dissimilarity Analysis (6 Pt. Window)
SMWA uses a z-score to identify dissimilarity between halves of a moving window. In this
case, the z-score represents the degree of difference in tree species richness three points to left
and right of each subject data point. This plot highlight several important themes in the
analysis. Data problems (far left), ideal response (~pt 23), and issues of scale (~pts. 35–41).
91
Moving along the results graph, the numbered z-score bars correspond with the numbered
data points. The SMWDA results are derived strictly from the TBEVM data. The border region
predictions are presented for reference only.
Beginning at the far left portion of the results graph, the results loosely follow the
predicted pattern until data point 23. This portion of the results set is the least consistent with the
Maxent predictions. This is likely due to some variance in the Maxent predictions. It must be
noted that data points 4-6 sit atop a ridge that marks the Tahoe Basin boundary and the northern
extent of the prediction surface. A small portion of the area north of the ridge was inadvertently
included in the sampling region. This small data gap and perhaps some edge effect may explain
some of this inconsistency. Additionally, the TBEVM data runs coincident with a predicted
border region (points 9–19). The results in this area indicate window half dissimilarity near
expected values as opposed to a sharp peak. It is likely that sharper peaks would be produced by
a bisection of the predicted border area.
From point 23 through approximately point 50, the results detect border regions as would
be expected. Sharp peaks correspond with predicted borders and negative z-scores correspond
with highly homogenous areas.
The final section of the results set (50–67) is interesting. The area is a series of ridges in
a managed, but primitive (non-wilderness) area. Slightly abrupt border regions are predicted
along the ridges. This is ecologically logical given some rain shadow on the lee (eastern) side of
the ridges would likely alter the predominant species community. The results set detects a series
of alternating borders and homogenous areas that is highly consistent with the model prediction.
The results of the SMWDA analysis are not perfectly aligned with the model predictions
nor is the analysis procedurally optimal. Given this, the existence of species richness border
92
regions cannot be conclusively validated; however, this analysis did consistently detect borders
and homogenous zones that align with the model predictions. For the purposes of this thesis,
these border regions will be considered valid, however extended research is necessary to further
validate their existence.
Chapter 5, Discussion and Conclusions expands on the discussion presented with these
results, and address each specific research question. Further, it provides some discussion
regarding how this thesis relates to existing literature and finally provide some suggestions for
further research.

93
CHAPTER 5: DISCUSSION AND CONCLUSIONS
A good deal of discussion is integrated into the results chapter of this thesis. As a result, this
chapter focuses on providing summary answers to the proposed research questions, discussion of
this research as it relates to the existing species richness literature and finally suggests avenues
for further research.

5.1 Research Questions
The research questions posed by this thesis aimed to explore the utility and validity of a Maxent-
based procedure to produce a species richness surface for tree species in the Lake Tahoe Basin,
CA/NV. The method moves beyond creating a probability surface for each possible species
richness value and eliminates areas of homogenous diversity from the representation. That is,
pixels containing more than one range of tree species richness are presented as border regions
between homogenous tracts of species richness. Thus, research questions address the validity of
utilizing Maxent to extrapolate species richness from sampled data and environmental variables,
whether or not border regions are meaningful entities and if the resulting surface is a useful tool
for use in forestry research and management.

5.1.1 Can the Maxent maximum entropy modeling package make valid predictions of tree
species richness patches?
A 2008 study examined the use of maximum entropy and state variables in macroecology (Harte
et al. 2008). Harte et al. make three observations that are relevant to evaluating the success or
failure of the species richness predictions in this thesis. First, they note that, as a procedure, the
maximum entropy method has been applied to many areas of science and that it is a proven
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method for inferring “most likely probability distributions” where knowledge-based constraints
are incorporated into the procedure. (p. 2701–2). Second, the application of maximum entropy to
a complex system requires only a numerically defined entity (that need not be narrowly defined),
and a set of constraints on the probability distributions (p. 2702). Finally, where assumed
constraints fail to provide an adequate prediction, then either, some constraints did not hold or
additional constraints must be explored (p. 2709).
Observations by Harte et al. (2008) directly address the novelty of using Maxent to
predict species richness. Specifically, they acknowledge the use of maximum entropy as
widespread throughout the sciences and that studied entities need not be narrowly defined.
Indeed, Harte et al. opine in their own example that distinguishing between “species” or
“individuals” is unimportant—the critical criterion is that entities are numerically defined.
Species richness meets this requirement.
This thesis further addresses the requirements of Harte et al. with a thorough
investigation of constraints on species richness in the LTB. Candidate variables from the
literature were analyzed quantitatively and then ranked by their impact on diversity. The specific
contribution of each highly ranked diversity predictor on species richness was further explored
by arranging them into a conceptual model grounded in ecological theory. These efforts directly
address the knowledge-based constraints requirement espoused by Harte et al.
Finally, as Harte et al. (2008) indicate, the quality of a Maxent prediction weighs heavily
on the inclusion of constraints that adequately predict the data. This thesis utilized Maxent to
create SDMs for tree species in the LTB species pool and distribution models for species
richness “entities” (one model for each possible value). Identical constraints (selected for their
effect on diversity) were used for both procedures. Initial assessments based on local knowledge
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indicated the surfaces generally reflect known species patterns in the LTB. Objective
assessments (AUC, dominant species overlay), however, indicate the Maxent predictions of
species richness entity distributions outperformed individual species SDMs. This is a positive
and expected outcome for two reasons. First, given the predictor variables are tailored for
diversity, not individual species, valid species richness distributions should outperform
individual SDMs. Second, high performing species richness predictions, based on environmental
factors separate from competitive factors affecting individual species, support the Neutral Theory
notion that species richness arises from a landscape patch’s ability to accept the random
colonization of a specific number of tropically similar species. That is, the system that defines
species richness patterns is distinct from the systems that define individual species distributions.
In sum, the distribution models created in this thesis strongly support that Maxent, given
appropriate environmental variables, can validly predict ranges of species richness if certain
ecological theories are accepted. Theories such as Hubbell’s Neutral Theory (Hubbell 2008) and
shifting mosaic-steady state (Borrman and Likens 1994) are controversial (Perry 2002). The
evidence, therefore, does not necessarily indicate that Maxent is the best tool for predicting
species richness, just a valid one.

5.1.2 Can the location and properties of border regions between Maxent predicted species
richness ranges be derived from Maxent output and if so, are they valid?
Two methods for arriving at a species richness distribution surface were investigated in this
thesis. The primary method, stacking and subtracting Maxent species richness ranges, produces
patches most correctly defined as “border regions.” Stacking and then summing individual
SDMs displays areas that border homogenous zones of species richness, but it does not isolate
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them. This is evident in Figure 29 where the species range method model is arguably more
cluttered; yet does not provide significantly more information. As to the capability of deriving
border regions, the answer is yes; however, the species richness method is more effective at
isolating them.
The more important component of this question pertains to validity. The concern is that
overlapping ranges of predicted species richness might reflect simple variance in the prediction
algorithm rather than legitimate ecological entities similar to an ecotone. Border region
validation relies on an analytical technique called split moving window dissimilarity analysis
(Cornelius and Reynolds 1991).
SMWDA is a technique designed to locate borders and ecotones by identifying
discontinuities in ordered ecological data. The TBEVM data used in this thesis are not
specifically ordered; however, a transect of these data that is approximately linear and covers
several suspected border regions was extracted for analysis. The results (Figure 31) are mixed.
The analysis identified several patches as discontinuities, strongly implying that they are
legitimate borders. Conversely, several patches were either not detected or not detected
consistent with the predicted abruptness. In these cases, plausible explanations such as edge
effect or patches running parallel to the transect decrease the impact of these inconsistencies.
Hennenberg (2005) reported similar issues with edge effect and detecting ecotones that are not
perpendicular to the transect. Still, these inconsistencies as well as the analytical limitations of
the TBEVM dataset cannot be completely discounted. Therefore, the best conclusion is that
border regions are likely to be legitimate entities; however, not every suspected border region
identified by this method is necessarily valid.

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5.1.3 Can the use of Maxent and a GIS produce a valid and broad scale representation of tree
species richness?
This is the penultimate question of this research. Broken into its three parts, the first element asks
if Maxent and a GIS can produce a representation of tree species richness. The answer is a
resounding yes. In fact, this research created two distinct representations using two different
techniques that are functionally equivalent. Further, it was demonstrated that the Maxent
surfaces are malleable enough to undergo substantial post-processing in a GIS, extending their
utility beyond merely defining the range of a species or other entity.
The second element, validity, is less conclusive. The best answer is probably. As
detailed by the previous two research questions, there is good evidence that Maxent produces a
valid prediction; however, its validity requires the acceptance of several ecological principles
that are heavily debated in the literature.
Lastly, the spatially explicit output and wide spatial scope of these models, if considered
valid, represent a significant tool for addressing the persistent problem of scale in species
richness applications. Patterns of diversity may be investigated as they vary from a few pixels
near the resolution limit of the surfaces all the way out to their full extents.

5.2 Discussion
This section delves briefly into the literature to assess two issues. First, why compiling these or
similar models would be of value to forest managers and researchers and second, how this
research meshes with similar studies.
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5.2.1 Applicability of Species Richness Models to Forest Management
Looking at the final species richness models produced during the course of this research (e.g.
Figures 23, 28 and 29) it is evident that management policies play a heavy (though not exclusive)
role in determining the final species richness structure of tree species in the LTB. For instance,
species richness border regions often parallel the edges of management zones (e.g. along urban-
wildland interface). In other cases, management zones (e.g. wilderness) encompass patterns of
diversity that visibly differ from adjacent areas. Interestingly, in no case does a jackknife
analysis indicate that management style is the most significant influence on species richness.
Clearly, human managers cannot meaningfully affect factors such as elevation or aspect.
Management style is, however, a forest manager’s best opportunity to influence diversity in the
interest of forest health.
The question then, given the multitude of factors and prescriptions available to forest
managers, is why species richness matters and how models such as these are helpful.
Invasive species are a matter of great concern in the LTB (LTBMU and USFS 2007,
LTBMU 2013, Taylor, 2014). A recent study indicates that high species richness relative to the
available species pool correlates with higher invasibility of adventive species (Akatov and
Akatova 2013). This is seemingly counterintuitive; however, it does correlate with the
contemporary ecology of the Tahoe Basin. High species richness along Lake Tahoe’s eastern
shore, is accompanied by (or perhaps due to) ongoing succession of Jeffery Pine stands by shade
tolerant fir species (Taylor 2014). Managing diversity-connected issues such as this is more
complicated than it may seem. The issue of scale in diversity issues is again applicable. Issues
such as succession are often rooted at regional or even geographic scales (e.g. climate change);
however, land managers most often operate and make decisions at the human level. Models such
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as these can highlight diversity patterns at multiple scales or perhaps reveal “hidden
heterogeneity” that provides important clues toward addressing unwanted change (Bestelmeyer
et al. 2003).
The model proposed by this research emphasizes the identification of ecotone-like
structures. The purpose and value of identifying these structures in the context of forest
management moves beyond decluttering the surface (although that is beneficial). The prime
utility of identifying and validating these structures is that they represent points of change within
the forest ecosystem. In this case, change in tree species diversity.
Changes, whether due to local urban development or global climate change, are points of
heavy interest in distressed ecosystems such as the LTB. A seminal article on Sierran ecotones,
Heath (1971), illustrates their use. The authors plotted the movement of an ecotone across a
number of years. They noted that it traveled linearly and varied in size, shape and species
composition without any sign of retrograde movement. The authors could not hypothesize a
specific cause; however, they stressed that this was an important phenomenon and urged further
research.
More recent research suggests the vertical movement of ecotones (i.e. upslope) are
indicators of climate change. Specifically, thermally regulated ecotones such as at the alpine-
woodland interface are indicated for this purpose (Kupfer and Cairns 1996). Bekker and
Malanson (2008) present several hypotheses for lateral patterns in forested (specifically sub-
alpine) landscapes. Winds, topography and seed dispersal are common themes; however one is
of particular interest to ecotonal movement.
The authors describe a process of “wave mortality” where high tree mortality in one
patch begets mortality in adjacent communities. This is an interesting insight for heavily
100
managed ecosystems such as the LTB. Common causes of patchy tree mortality in the Tahoe
Basin are natural occurrences (e.g. insect attack, avalanche) or human activity (e.g. prescribed
thinning or fires).
In essence, wave mortality and climate change returns the present discussion to one of the
primary determinants of species richness as discussed in Adams (2008)—disturbance. If
disturbance drives change in diversity, then models capable of pinpointing where and at what
scale change is occurring within an ecosystem are valuable tools for land managers. These
models are unlikely to pinpoint the underlying drivers of change, but a series of these models are
more than capable of identifying points of change that may have otherwise gone undetected and
warrant further management attention.
Finally, recall that these models are not mere surveys of known species richness. They
are predictions drawn from sampled data. As such, advanced versions of these models could be
capable of creating what-if scenarios. This serves two purposes. First, it overcomes the inherent
downside of temporal studies. Forest landscapes evolve across decades, so identifying the
effects of management efforts within the real-world landscape are inevitably delayed by many
years. Second, the ability to test prescribed treatments in for their potential effects would be an
extremely valuable resource.

5.2.2 Relationship to Recent Research
Chiarucci (2012) provides commentary on a piece of research cited throughout this thesis, Xu et
al. (2011). Chiarucci laments that despite Xu et al.’s exhaustive labor evaluating the species
richness prediction capabilities of a dozen area-based and non-parametric methods, no approach
succeeded in hitting an accurate mark. That is, every procedure tested by Xu et al. either over or
101
under estimated true species richness. Chiarucci further cites many similar research efforts over
the last two decades—including interpolation and extrapolation—and decries the fact that no real
progress has been made. Chiarucci concedes that truly accurate species richness predictions are
limited to areas that do not extend far beyond the area sampled.
Chiarucci’s commentary expresses “difficulty” in the sense that highly accurate
estimators are elusive despite decades of research. This research addresses difficulty in the
context of accessibility. It is fair so assume the accuracy range of the procedure reviewed by
Chiarucci represent the state of the art. No quantitative assessment of accuracy was conducted as
part of this research; however, empirical assessments were positive enough to reasonably assume
the output of these models fall within the accuracy range of other documented procedures. A
common thread among species richness prediction algorithms in the literature is that they are
complex and difficult to perform without high-level mathematical knowledge and skills. The
models in this thesis can be created with intermediate geospatial skills. As such, this research
contributes a procedure that provides access to the state of the art for managers and researchers
with modest mathematical backgrounds.
The accuracy of the models in this research is likely related to the dense presence-only
data used with the Maxent application. TBEVM data meets the best accuracy criterion espoused
by Ciarucci (2012) as it covers much of the Basin. Very little upscaling is required by the
Maxent algorithm. Its primary function is to etch out the most probable boundaries of species
richness homogeneity based on background factors and within the dense dataset. This is clearly
a less rigorous task than extrapolating or interpolating between sparse (and possibly inaccurate)
field samples.
102
Most species richness prediction algorithms depend on quadrat or transect data (e.g.
Dupuis and Goulard 2011). Field collection of species richness data is tedious at best and is
commonly fraught with significant biases. This leads to datasets that are insufficient,
inconsistent and often inaccurate (Engemann et al. 2014).
The TBEVM data used in this research is remote sensing-based. Remotely sensed data is
capable of providing much more study area coverage than field-collected samples. A good deal
of research is centered on deriving species richness from remotely sensed data (Camathias et al.
2013, Cord et al. 2014, Fricker et al., 2015, abstract). Applying these dense, remotely sensed
datasets to mathematical models has the potential for increasing accuracy in both area-based
extrapolation and distribution models.
Remotely sensed datasets are not an accuracy cure-all, however. Classification
algorithms limit the accuracy of satellite imagery. As noted in Chapter 3, TBEVM for example
is incapable of discriminating Jeffrey Pine from Ponderosa Pine. In effect, one type of bias is
being exchanged for another. The increased density of remotely sensed datasets, however, is
likely a reasonable tradeoff for these biases.
Lastly, the work of Dubuis et al. is regularly cited in this thesis. Their work provided a
non-spatially explicit framework for the conduct of this research. Dubuis et al. note that directly
estimating species richness from environmental factors eliminates knowledge of specific species
composition. They list this as a serious limitation. That is not necessarily the case. Human
nature inevitably induces bias into decision-making. Anonymous data provide an opportunity to
support or refute management paradigms without bias for particular species at least until field
surveys are conducted. This is a good thing. Providing an opportunity to reassess or reaffirm
management practices based on blind data may be the most significant outcome of this research.
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5.2 Suggestions for Future Work
This final section provides a few suggestion for making this work more complete, as well as
deriving additional benefit from the results of this research.

5.2.1 Modeling Realistically Dense Data
The extremely dense TBEVM dataset was purposely chosen for its expansive coverage of the
LTB. The dataset is older; however, that limitation was countered by the high likelihood of
creating an accurate surface. Even with emerging remote sensing techniques, the likelihood that
users of this model will have access to extremely dense and carefully vetted data is unlikely. An
investigation into how the model degrades with decreasing density is worthwhile.

5.2.2 Field Validation
Time restrictions combined with the winter season precluded field validation of the models in
this research. A field investigation should determine which species richness borders are
accurate, which are not and collect evidence that sheds light on variables that affect the
predictions.
Border regions predicted by the model, particularly unexpected ones, should be
investigated for a biological or ecological explanation. This research extension could provide
valuable insight to forest managers interested in incorporating diversity indicators into their
decision making processes.

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5.2.3 Temporal Study
The study of borders and ecotones is most useful when done over time. An animated time series
of models will provide a level of insight into the evolution of diversity around the LTB that a
single snapshot cannot approach. Clearly, the most significant barrier to this research extension
is the availability of adequate data. As mentioned in the preceding section, however, remote
sensing of species richness is a heavy focus of recent research. Options from the latest literature
should be explored.
Alternatively, the model could be expanded to include the capability for creating the
what-if scenarios described in the previous section. Carefully altering existing data and then
inputting them into the model could accomplish this. Whatever the method, a temporal
expansion of this technique is necessary to extract its maximum benefit.

105
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APPENDIX 1: COMPLETE JACKNIFE ANALYSIS FOR SPECIES RICHNESS
This appendix contains the Maxent jackknife analysis charts against AUC for each
species richness SDM.

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Abstract (if available)

Abstract The Lake Tahoe Basin, California/Nevada is the setting for evaluating a species richness modeling technique that is both accessible and provides an apparently unique approach to studying forest diversity patterns. Species richness, the total number of species of a focal group present in an ecological community without regard to individual taxa, is an important indicator of biodiversity. Despite its importance to researchers and natural resource managers, predicting species richness patterns in forested landscapes is difficult and therefore, not common. The computationally powerful yet highly accessible Maxent package, specifically designed for modeling species distributions, is used to predict homogenous patches of species richness by treating species richness values as individual “species.” Areas where ranges of homogenous species richness overlap are then isolated and displayed as “border regions” similar to ecotones. Nowhere in the ecological literature is Maxent used in this manner, nor are transitional zones between regions of species richness viewed as spatial entities. Therefore, this thesis investigates if Maxent can make valid predictions about species richness and if areas where species richness predictions overlap constitute transition zones. To validate the model, traditional species distribution models for each included tree species were created using Maxent, stacked and then summed to produce a comparable species richness surface. Similar patterns between the two models indicate that Maxent accurately predicts species richness from environmental factors. Border regions were validated as legitimate spatial entities using split moving window dissimilarity analysis—a technique used to identify ecotones. Results indicate that using Maxent for this application is very likely valid and species richness border regions represent a promising spatial entity for studying diversity patterns. This spatially explicit approach provides an accessible method for studying species richness patterns at multiple scales. Further, a temporal series of these models provides a method for examining how diversity changes over time.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Pollock, James J. (author)

Core Title A Maxent-based model for identifying local-scale tree species richness patch boundaries in the Lake Tahoe Basin of California and Nevada

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 06/17/2015

Defense Date 04/13/2015

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag ecotone detection,ecotones,forestry,Lake Tahoe,Maxent,maximum entropy,neutral theory,OAI-PMH Harvest,species distribution model,species richness

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Longcore, Travis R. (committee chair), Kemp, Karen K. (committee member), Lee, Su Jin (committee member)

Creator Email jpollock@usc.edu,jpollock1970@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-571163

Unique identifier UC11300071

Identifier etd-PollockJam-3470.pdf (filename),usctheses-c3-571163 (legacy record id)

Legacy Identifier etd-PollockJam-3470.pdf

Dmrecord 571163

Document Type Thesis

Format application/pdf (imt)

Rights Pollock, James J.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA